It usually starts in one of the reds, and spreads inch by inch over the course of a few weeks. It gets raised and itches like crazy, and lasts 2-3 days in a small area before spreading. It's a real struggle not to scratch.
Unfortunately 1/4 of my body is essentially one giant tattoo, so it's got plenty of room to spread. The small patches of surrounding un-inked skin are completely unaffected, so I suspect it's definitely the ink.
When the first red tattoo I got REALLY swelled up, the tattoer told me it's rare but he'd seem it before, and some people don't take red well. From what I understand the red ink 20 years ago was formulated differently than now. I'm not entirely convinced it's just that color, because all of mine itch.
I think though, I'd phrase your hypothesis as those with tattoos likely have a different risk to reward calculus.