Obviously you are in a much better position to speak for TDI than me, but in my AN/DP and Trimix classes, I was taught to use a closed fist to indicate stop (no extended pinkie) and then indicate time.
Furthermore, to end the stop and move to the next, with TDI I was taught to give a thumbs up with my right hand but cover it with an extended left hand giving a ceiling for the thumbs up. With GUE, the signal to move up is one handed and with an extended right hand simulate moving your hand up a level.
I don't speak for TDI at all... I just know their standards reasonably fluently. What you were taught, I guess, is OK, but not what's "in the book." Just saying. The thumbs-up with a hand on top is used on occasion, but the one-handed "step-up" motion is more conventional... at least, in my opinion and experience. I used to fight with Larry Green on one issue and one issue only when it came to standards and training. He taught that the signal to turn a cave dive was a thumbs up. I disagreed. A thumbs up means the rottweiler has hit the fan, let's get the heck out of Dodge. Index finger pointing up and tracing a circle means "Everything is cool but it's time to turn the dive... so who knows?
My view is that ANYTHING that adds to the possibility of confusion... especially with regards communication... is counter-productive. When it comes to hand-signals, what cave divers (and their open-water cousins) have been taught for the past 20-odd years does not need fixing. Unfortunately, that message is lost... sometimes... just like standard hand-signals get lost in the noise sometimes.
HOWEVER, all that aside, I am still waiting to hear from the OP about the source of the information he and "his family" are using to construct a new onLine resource.