The lip of the button needs to be able to slide or rotate in the groove as the wood moves (i.e. top expands and contracts), so at least slightly looser than a "snug" fit in the groove. The width of the groove is not critical as long as it is wider than the lip. The lip of the button should be snug (not super tight) against the top of the groove, keeping the top firm against the aprons/base. It will still move before the wood separates. The button is made so the thickness between its top, and the top of the lip is slightly less than the distance from the table top to the top of the groove. This allows you to adjust the "snugness" of the fit by the screw tension. Otherwise the table top will be loose to the base.
If you glue the buttons to the top, you will not be able to remove the top in the future for repair, refinish, or even take down for transportation, without chiseling them off. There is also the chance that the glue will get into the groove, defeating the purpose of using the buttons in the first place. Gluing it also prevents you from using the screw to tighten the top a bit more if it shrinks enough to become loose to the base.
If you haven't already glued the base, you can just run a dado on the inside of the aprons and then make the buttons to fit. This allows you to locate the buttons where ever you want, and to relocate them if some gorilla snatches the top hard enough to strip out the button screws. (Or if you strip out the screw when installing. DAMHIKT LOL)