My residence is a town home built in the late '90s, thus having non-tamper-resistant outlets. I assume that they are grandfathered in NEC? Am I required, by NEC, to install tamper-resistant when replacing an outlet?
Yes. If you're not making changes, there's no requirement to swap them out. If you are changing out the receptacles for any reason, you'll have to install tamper resistant receptacles. You cannot replace the receptacles with non-tamper resistant receptacles (technically).