Having a quick fill in many cases is a good thing. It won't matter how fast the system fills up as long as the overflow is big enough to keep the level where you set it.
That's the only real worry with flooding and such!!!
As for water in the bottom of the tray, are your cubes suspended above the tray or resting in the bottom of the tray?
If they are suspended, then it's no big deal at all. If they are in the tray, then the rockwool might stay too wet. Correct that by putting the rockwool into pots and filling the pots with some media like clay pebbles or hydroton in order to put them at the right height.