Generally speaking, the various boosts (attack, defense, production, etc) provided by some event buildings increase at certain Ages (but not necessarily with every Age), while others don't. Amount of coins, supplies, medals, population, happiness typically increases each Age - but amount of fp's rarely increases. Goods output number is often unchanged, but you get the goods corresponding to the Age of the building (not the Age you're in).
So, some buildings you may want to use 1Up kit (increases by 1 Age) or reno kit (increases to your current Age no matter what Age it was before) when you advance an Age. Others you may leave as is. Each building functions fine irregardless of what Ages they are, even if part of a set
You can check any building's (or most anything else) stats for every Age via the fan wiki...
https://forgeofempires.fandom.com/wiki/Forge_of_Empires_Wiki