Juan Mata's mum had never been in a helicopter before. Juan Mata had, but this was different. "I'd done the tourist thing, flying along the Grand Canyon and over Manhattan too but that was the first time it was a 'necessity'," he says, recalling the jokes from friends stacking up on his mobile.

January 2014 and "Jonny Kills" (the literal translation of his name, and his nickname in England) had embarked upon a new mission, racing north, with his mum and dad on board, handkerchief neatly tucked into his breast pocket. At £37.1m he had just become Manchester United's record signing. "It was all a bit surreal," he says.

Waiting for him was David Moyes. So too was Ryan Giggs. Mata's hero as a kid was the Real Oviedo midfielder Roberto Pompei. In Spain, that is; in England, it was Giggs, the winger whose shirt he sought when Valencia faced United in the Champions League. Now Giggs was his team-mate, soon he would be his manager. "I told him [he was my idol] when I arrived," Mata smiles. "And he said to me, joking: 'I'm really happy you're here … but I'm a bit sad too. Now I'm only the second best left-footer here'."

"The first days at a new club are always a bit strange but when you have someone like Ryan saying that it eases things," Mata says. "And it really helped that David de Gea was here. He'd been sending messages all week: 'What's happening?' 'When are you coming?'"

"It was a long week," Mata admits. "Mentally, it was complicated. It was hard to leave Chelsea and I'll always be grateful, but at the same time I was joining a great club. I spent virtually the whole time at home with my family, trying to stay calm, waiting, watching time pass, watching films and series, checking the phone. I went to the gym to make sure I didn't lose shape, because I hardly trained [with the team].

Lots of team-mates are friends and they call. Not to gossip, but to ask how you are, to be by your side. I'm still in touch with people at Chelsea: there are good people in that dressing room, friends for ever. Everything depends on the club more than the player: the quantities, the paperwork."

Perhaps the surprise was how apparently amicably the deal was concluded, testament to the skill of the agents handling negotiations. Mata played his part too; Chelsea supporters admired his handling of it, appreciating the letter he addressed to them. "Class", was the conclusion.

"I didn't do that for image's sake," he says. "I wanted to feel at ease with myself, do the right thing, express how I felt about Chelsea. In the end, everyone was conscious of what the situation was. They realised this was the best solution for everyone. I will always be grateful to Chelsea, to the players, the directors, the owner, the fans …"

Was it necessary to leave? The helicopter ride had the feel of a rescue mission about it, but did Mata feel like United had rescued him? There's a pause. Mata speaks calmly, slowly and thoughtfully.

"Like any footballer, I love to play, I love to feel important, I love to enjoy the game. I'll always be proud to say I played at Chelsea, at Valencia, in the youth system at Real Madrid, in the youth system at Real Oviedo, and for United …"

Spain, too. Mata is a world and European champion and a second World Cup was surely a factor. "It's an objective, of course," he admits. "You see the World Cup getting further away and you want to play. That's very important. But a decision like this is not a six-month decision, it's a four-year decision. For both teams and for me it was the right moment, but it was a long-term move, not just six months."

"When you're not playing you don't always have the opportunity to join a club like Manchester United, prepared to pay a barbaridad (fortune) to sign you. It's hard to find a club that does that, especially for a player who's not playing. It gives you enormous confidence, to be United's most expensive player is a big deal and makes me feel I have played well in England. I'm grateful they think so highly of me."

If United did, why didn't Chelsea? Mata has won an FA Cup, the Europa League and the Champions League in England. Two years running, he was Chelsea's player of the year. Again, the response is thoughtful, delivered softly and evenly. "There are lots of players who train hard but don't play and can't explain why. I was put in a situation in which, fortunately, I'd never been before. Perhaps you don't appreciate that if you always play, so going through it makes you see things differently. That's a good thing. I learned."

"I tried to be positive and trained the same as ever. The decision's nothing to do with the player. All I could do was be professional and be available."

Did you ask José Mourinho why you weren't playing? "No." Why not? "Because I didn't consider it opportune." Did he offer an explanation? "No. We never talked about that. Nor would we. When I played, I played. He would give me instructions. There are coaches who explain but others who don't think it's necessary. That's all."

Manchester United's Juan Mata. Photograph: Jan Kruger/Getty Images

United were a different story. "David [Moyes] called me and said they needed a player like me who makes the team play, who could offer fluidity and provide assists and goals. He told me he thought I could play in any of the three positions behind the striker. I said, yes, I'd played in all three during my career. But in negotiations like this, it always takes a long time. Then came the journey in the helicopter. It was all a bit unreal. And then after just two days' training, I was playing for Manchester United."

Mata provided an assist in his debut against Cardiff. He has since scored five times and provided four assists. Only Wayne Rooney and Robin van Persie have more goals and only Rooney has more assists this season. He has been player of the month for two of the three months he has spent at the club, even if he has sometimes appeared on the right, the least natural of the three roles.

"I don't think that's true," he counters. "I don't consider myself a right-winger but it offers me the chance to come inside and that way I have a broader field of vision. It's true, though, that the position that I play best in is media punta . You get into the area more, you provide more assists, more goals, but I can play in any of the three."

If Louis van Gaal arrives as manager – and Mata is quick to insist that he has no idea if he will, saying that players have not been consulted – another option opens up: in a midfield three a little deeper.

"I played there for Spain a couple of times. It's not my normal position but any role which involves having a lot of contact with the ball suits me. You're more comfortable, more in the game, with every touch."

There is an enjoyment about Mata as he talks of United, of visiting the club museum, of Giggs stickers, of Old Trafford, but these have not always been comfortable weeks. This is the first season he has finished in England without a trophy. Moyes was sacked; Giggs came in. In three years, Mata has had six managers in England, often seen in Spain as a haven of patience. "So you're saying it's my fault?!" he laughs.

Explaining it is not easy. "It's complicated when someone's been at a club for almost 30 years, it's a dramatic change. Things haven't worked out," Mata concedes. "I remember coming here with Chelsea and it was almost impossible to win at Old Trafford. Thirteen months ago United would be losing 3-0 and they'd win 4-3. Now we're losing 3-0 and a comeback feels impossible. Maybe there was a loss of confidence, maybe the club found itself in a position it has not been in for years and found it hard to react.

"When a manager goes, the feeling is sadness; there's disappointment and a sense of responsibility. 'If we'd played better, he wouldn't have been sacked.' But the sensation is more general, it's not necessarily focused on the manager. I'll always be grateful to Moyes for bringing me here."

And then came Giggs. "On the Monday he's dressed as a player, on the Tuesday as the manager," Mata says. In a suit? "No. But he was wearing the manager's training top." Did the players suddenly have to call him "gaffer"? Mata smiles. "Giggsy. 'Gaffer' would have felt a bit odd."

"He's calm, shy. He's not a big talker but when he does talk people listen. When you've been here for 20 years, when you know United intimately and what it takes to win, you command respect. He said: 'I'm taking charge for four weeks, we're going to try to do things the right way. I know the ability this team has and I'm going to ensure everyone has a fair chance. We have to be aware that we're representing an enormous club with millions of people behind it.'"

Could missing out on the Champions League be an advantage for United next season? "In the league? Definitely. Of course, I would rather be playing in the Champions League but if we take Liverpool as the example this year; there's a team who have fought all the way to the finish without having played in the Champions League and that might have helped them. Why not? That might be good for the Premier League, yes."

Mata chose where I interviewed him, 20 minutes outside Manchester, because it was quiet. Or so he thought. Fans have travelled in for the weekend's game and the requests for photos and autographs are as constant as the excitement and the goodwill. "There's definitely a 'wow, it's United!' feel," he says. "Old Trafford is fantastic, absolutely huge, and the fans are incredible.

"There are huge demands here. If you don't win the league one year, you have to win it the next. We're all responsible, not just the coach. Next season we have to demonstrate that the club has not lost its essence, its mentality or its competitiveness, that Manchester United has not lost its identity."