It's fine as long as you don't store it in anything that creates moisture from the humidity. I've seen morons store ammo in ziplock bags in a shed.....That was obviously an issue with the condensation from plastic.
My dad (gunsmithing and reloading, both hobby and as a business) worked out of a separate building with just a window unit for A/C here part time (only when he was in there) in Florida for 20 years. Never had an issue with any ammo, black powder, nothing. His larger gun safe with all kinds of expensive shit was in that building, never had an issue with firearms rusting either (including my great grandfathers Winchester from the 1890s). Just keep ammo in the cardboard boxes they came in and no worries. If we have no problem shooting 50+ year old ammo found in my grandparents home (also here in Florida), no issues.
Fun tidbit, my great grandfather called that Winchester his, "nigger gun"
