Citibank is closing down branches in its fastest-growing region — but the American banking group said that'll actually help it do better than ever.

The lender's consumer business in Asia, its largest outside North America, registered its seventh consecutive quarter of growth in the first three months of 2018. Underpinning that momentum is the growth in Citi's cards business, which the company said was largely a result of its decision about three years ago to "digitize" the way it operates.

That means spending more of its advertising budget on digital ads, forming partnerships with e-commerce players and social media platforms, and building systems that allow people to apply for cards online, said Sergio Zanatti, Citibank’s head of cards and personal loans for Asia.

"In the past, customers need to come to the bank, what we’re trying to do is flip that completely: We want to be accessible to you as a customer in the place and in the way you prefer to interact. We want to be present in the place or ecosystem that you play and live," Zanatti told CNBC in an interview last week.

That’s a move away from waiting for customers to show up at physical branches and relying on large sales forces to get people to sign up for credit cards, he added. Instead, greater use of data analytics and digital channels allows the bank to target the right customers more efficiently and keep them around for longer, he explained.