I haven't done fondant decorations on crusting buttercream and I need tips. I have a client that wants this cake and I'm worried all the dots will fall off. Do I refrigerate first, apply with anything special, etc.? Any advice would be appreciated! Thanks.

Do NOT refrig cake. apply b'cream; allow to dry naturally. Depending on the recipe used it can take 10 min to several hours.
Using a small round tip (about #3) pipe an open circle on each circle/dot of fondant and stick it to the cake.
That circle will act like a suction and hold the pieces in place well.

Thanks kakeladi. Do I pipe with the same buttercream?

I'd just dab the backs with vanilla extract or piping gel.

Just brushing the back of each dot with water will make it adhere to the crusted BC. I did that with a Bingo-themed cake a few months back, with disks like Bingo markers on the side. None fell off.