I live in the Caribbean and I use American buttercream under my fondant too. I usually put my buttercream covered cakes in the fridge overnight and take them out the next day into an air conditioned room about 30 minutes before I’m ready to cover them with fondant. They will condense a little so all you do is take a paper towel and gently press on the cake to remove excess water. Now you have a firm cool cake to work with and you don’t need to brush the buttercream since it’s already wet. The fondant goes on and there’s no bulge.