We try to dump the black tank when we have access to water for the black tank flush. So I say, if you can't flush the tank after dumping, then dump it before you go home. IF you have water hookup to run the black tank flush at home, then, IMO, it really doesn't matter when you dump.
We use that black tank flush, and often run two or three half tanks of water through it after dumping. I like a clean black tank
Our process is, pull black tank valve, let it drain. Run black tank flush for a few minutes, then close black tank valve and fill tank, using black tank flush, to 40% or so. Shut off black tank flush, and dump tank. Repeat a couple times, till no more tp or other stuff comes out.
When I see, through that clear elbow, water running clear enough that it looks fit to drink, I'm done.