It's so FLUFFY!!!!
I thought TT was still in beta. It doesn't randomize the player's mats.
What we did was remove all the pieces from the boards and unlock the mats. then we put them in the empty bag (at the corner of the board) and shuffle them. After that we start randomly drawing them from the bag.
Hope this helps.
Also, Tabletop Simulator's official version is really nice! Like it better than TT's at the moment.