I think you meant to turn the dough 90° (not 180° as stated).
Each fold, turn, fold multiplies the layers by 9. So after the envelope, then fold turn fold you have 9 layers.
Then refrigerate an hour, then roll out, fold, turn, fold, you now have 81 layers.
Am I supposed to refrigerate it again for an hour at this point?
The next roll out, fold, turn, fold yields 729 layers (not 2187). To get 2187 layers, you would need to roll it out again and fold into a long rectangle and then roll it out (without creating a square). Had I turned and then folded to create a square again, I would have had 6561 layers.
Is it necessary to refrigerate the dough for an hour in between rolling it out again each time before the fold turn fold step?