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Primers are in no way sealed in those containers so I would not keep them outside. I load in the house in a spare bedroom.

I left my stuff in the garge for years with no issue. I kept them in air tight ammo cans , I now have them in side where I can actually load for more than a few mins without having sweat in my eyes.

I reloaded in the garage for years before I built my new bench and moved it into a now empty room after my last kid moved out. I stored my powder there as well. It stayed pretty cool, but was very, very cold in winter. Now everything is inside.

I see that to OP is in Texas, so cold probably isn't an issue. I think that if I lived in Texas, I would keep my powder inside.

Ammo, powder, and primers are all stored inside in a number of ammo cans, all with a packet of silica gel inside.