*Office Jerks
Some good finds there.
The adhesive is yellow/white in colour. I have never had too much issue with coming through. Once it happened many years ago when I sprayed too heavy in one spot. Lucky it was not in an obvious place. I didn't wait for it to tac off enough.
In Australia, it dries much faster than the can suggests so plan well and work fast.
If you want a thin foam backing, I use scrim foam. I get it in sheets from foam supply places (not Clark Blubber). It is used in plumbing for wraping pipes. 1 or 2mm thick.
I get the foam down on the trim, then I get the fabric down.
Don't lay it all at once. Keep it up at one end and use your hand to gently firm it down in a swiping motion.