I've never repaired bike tubes using rubber cement, only the vulcanizing solvent. When people call this stuff "glue" or "cement" they're not being technically accurate. How it actually works is by chemically softening the tube, so the patch will become welded to it, so to speak.

It is analogous to welding vs. brazing metal. In welding, we're actually melting the base metal. The molten metals from both pieces mix, and when they cool, they've become one. With brazing, only the filler material melts. The base metal gets hot enough to bond with the filler, but does not melt. (Incidentally, the technical difference between soldering and brazing is the temperature involved, which is dictated by the kind of filler metal you want to use, which in turn is generally dictated by the joint strength needed.) That's enough for today's lecture.

Anyway, the reason you wait a couple minutes for vulcanizing solvent to dry is because it's not acting like glue to form a bond. It's dissolving the outer layer of the rubber, which combines with the soft rubber of the patch to be very strong.