Don't know about alum, but lime settles pretty quickly. Once it's on the bottom swimming isn't an issue as far as I know.

From what I've read ( but don't rely on this) alum acts much the same way, since it attaches to suspended clay and settles it on the bottom.

I'd think after a few days you should be fine.

.10 surface acre pond, 10.5 foot deep. SW LA. The epitome of a mutt pond. BG, LMB, GSF, RES, BH, Warmouth, Longear Sunfish, Gambusia,Mud Minnows, Crappie, and now shiners!!...I subscribe!!