I was taught to dry the print (and flatten it) and the mounting board for a 1/2 minute in the press, allowing it to cool before attaching the mounting tissue and putting it back into the press for another minute.
I was never a fan of the "mount off center" aesthetic - I center my prints on the board. Square prints are also personal preference - square mats or rectangle - I generally use rectangle because that's the way the precut mat boards and ready made frames come (I guess that I'm lazy).
I like nice flat prints that don't get damaged, so I dry-mount them. If the galleries don't like matted prints, I suppose my heirs will lose out! Or when they throw out all my stuff they'll have to hire a larger size dumpster.