Here's what I've observed:
1. In an unmodded game (yes the bolding is important) tattoos will reset your sim's age to the beginning of the life stage they're in. They don't remain banned in dynasties for no reason after all. Same goes for getting a stylist's makeover. It probably has to do with technically getting thrown into CAS for those, as the Edit in CAS cheat can mess with ages as well.
2. The NRaas mod suite stops the age reset, as far as I'm aware. I'm not sure which mod it is (since I have many of course) but I know when I have all my mods in, tattoos and stylist appointments don't affect age.