I can only comment on the acrylic product in the plastic dropper bottles and larger plastic pots (which is, as far as I can tell, exactly the same product), but I have no experience with the 'Future Floor Finish'-killer that started off Army Painter back in the day.
It is as stated: a lot depends on the amount of wash applied, the room temperature and humidity, but overall, I'd say that the wash can be drybrushed over safely after about 15 minutes, give or take.
Longer drying times are always better of course. In fact I usually plan it so I apply a wash as the last activity of the evening/night, so it has plenty of time to thoroughly dry.
But when the heat is on and the blood is up, I usually set a mini aside for the abovementioned 15 minutes or so. Or not, if I'm batch painting an entire unit, because once I'm done with the last one, the first one is usually dry enough to continue.
Also, I once set myself a challenge to finish a set of minis in one hour's time, and then I simply used my wife's hairdryer
