How to put on houndstooth roof

Do the original houndstooth roof vinyl just sit on the roof or does it need foam under it? I keep gettin differing opinions. Any help is much appreciated

It glues to the roof. Foam is undesirable since it traps water and next thing you know the roof needs replacing because of rust.

What adhesive is the best?

I use 3M #1357. It takes about a quart to install a top and headliner.