When I use a tent (I use a bivy a lot of the time), I have always carried it in the rear rack. I roll it with the watertight floor on the outside. The body of the tent is typically no wetter or drier at the end of the day's ride than when I rolled it up.
If the fly is drenched I leave it out and roll it separately. If the tent is super wet and there is a dry portion of the day I often lay it out to dry during a break.