When you get a tattoo, your body recognizes it as a foreign object, so your lymph nodes start producing T cells and lymphocytes (aka: foreign object fighting cells...er...that's too long to type, they'll be referred to as "FOF cells")... so, anyways this is why your tat swells immediately after. So, eventually these FOF cells are like, "hey, it's just a tattoo. It's no biggie, we'll just leave it alone". So they just go through your blood for a bit before they end up in the spleen (this is where they die).

Now your lymph node knows how to attack ink (tattoos), so next time it experiences something inky (hair dye) your lymph node is like, "This is the same ink as before!!" so it produces an excess of FOF cells and these cells are like, "OMG! LETS KILL THIS DYE!" So they produce an allergic reaction to the dye.

So, it's not just the tatted area. You can tattoo your foot and have a reaction to hair dye. It's just because you're hyper sensitive and your "FOF cells" are on high alert.

A more tangible example of this is getting the flu. You get the flu once, it knocks you out. You're feeling like garbage. But then if the same flu comes around, your body knows how to kill it, so your body goes into flu killing overdrive (producing lots of FOF cells) and you get better quicker.