IIRC, in the base TM, the rule was the same as in base GP (ie: turn order from the first player).
The Fire and Ice expansion changed it to the (IMHO, much better) new player order = pass order.
Which, as stated is included as an optional rule in GP (and should pretty much always be used, again IMHO).
Ah ok. I didnt remember that.
I think if there ever will be a competetive GP-play (online or reallife) it will be surely be played with that turnordercard.