Although I used to be an IANTD instructor I've let that lapse and won't be renewing it, for a number of reasons unrelated to diving. I did the TDI instructor course but never bothered to send the papers in, as I couldn't see the point of duplicating what I was already doing for IANTD. I have considered signing up with TDI now I'm out of IANTD, but really I don't have the need. At the time I did all this (eight or so years ago) I was very unimpressed with TDI's standards, which fell a long way short of IANTD's. I'd love to know what they are now, but they're restricted and only instructors have sight of them (I can't imagine why, though IANTD have now followed suit). I wrote to TDI recently to ask some specific questions on standards but they directly refused to answer them, which I found amazing. So I don't know whether they now require dives on trimix as part of trimix certification (when I did their course years ago they could all be simulated). They also required way fewer "trimix" than IANTD did at that time - two instead of six (and that six often became eight).
I can only tell you what I was made to do. But, I think everything boils down to the instructor, not the agency...just like recreational diving. I picked mine because he is considered the toughest instructor in the Upper Midwest. I've heard that from multiple people and I even read on one forum from a boat captain that does tech trips in Lake Michigan that if he sees a card signed by my instructor (as well as another guy), he knows they are a well trained good diver. He also didn't pass me on my Advanced Nitrox and Decompression training this spring right away. I had to come back because he didn't think I was there yet. So, that must say something for him.
Anyhoo, I had to do my shutdown drill within a minute, remove both of my stages while maintaining my buoyancy...not touch the platform, follow a line horizontally for 50 feet on one breath blindfolded and...I'm forgetting something. I also know they require at least 100 minutes of bottom time, which I went well past. I did 2 160' dives for 10 minutes with simulated deco stops having to do all the normal drills after ascending past 100 feet like shut down a post due to a simulated leak, out of air drill, throw a bag (every dive), etc. My last dive was 180 feet for 15 minutes. That one I had to plan and lead (I had to lead all the dives. My instructor was just there as if he was the junior diver.) the dive. So, I ran two profiles through V-Planner and my instructor chose the one that would model his VR3 the most (I added a deep stop at 135 feet for 2 minutes) and we went diving with me calling the turn, gas switches, stops etc.
So, that was about it. Three days of diving with heavy emphasis on buoyancy control and self reliance.