It's hard to tell but they could be wafer paper or thing gumpaste.
Wafer paper will be more affected by humidity than the oils in buttercream, but it's best to be on the safe side and put them on at the last minute. Don't refrigerate a buttercream or fondant cake that has wafer paper on it because the condensation when you remove the cake from the fridge will melt the paper.
You can paint the back of the wafer paper flowers with a little melted white chocolate if you want to create a barrier between them and buttercream. Just don't refrigerate the cake with them on it.
Thank you for the advise about not putting the decorated cake in the fridge. I'd have probably done that.