Very nice basement plan. It really can be done either way, when my husband built our home he tiled first and put the cabinets over the tile, however I am already making plans for new "future down the road" flooring and wondering how that is going to work out with cabinets and quartz counter tops over the tile. If you never ever plan to remove the flooring then you can place your bar over the tile no problem. However a lot of builders tile up to the cabinets/bar. This saves on product and actually costs less in the end because you are not wasting product. Though because this is in a basement you might not want your wood bar directly on the concrete slab therefore putting tile down first might be the way to go. We are having the same talks right now about our future basement bar too. Knowing my husband he will lay the cabinets for the bar over the tile as it is less cuts and easier to do but costs more in the end.

I believe it really depends on your type of bar. Mine is faced with glass block and it was necessary to attach them to the concrete floor. It's a permanent structure, can't ever be moved.

If you know exactly where your install(s) will be, anchor necessary 2 x 4's (pressure treated) onto the concrete. These will be used to secure cabinets or structures via screws through their side(s). Then install your tile, atop of which the cabinets can then be set.