One minute more or less at a roughly 10 minute developer time is only 10%. That's why both your Tri-X and TMax 400 negatives print well (I assume you are printing, since this is not the hybrid, soup and scan forum-LOL).
Many ISO 400 films are no such thing. The only way you can check the true speed is to shoot a test.
The best thing to do when introducing a new film into your workflow is to test the film side by side on both one of your known good films and the new film, do an exposure series on each and process together (most 400 films process for about the same time, and yes I know there are a lot of exceptions, Kentmere 400 comes to mind for one example). Process together and then print all the prints in the exposure series on both your known good film and your unknown.
In my experience TMax 400 has a great deal of both exposure and processing latitude and Kodak for many years recommended no additional processing time for negatives shot at ISO 800, twice the official ISO rating. A good TMax negative will look thin compared to a good negative shot on a more conventional film, e.g. Tri-X.
My own personal settings? I shoot Tri-X unpushed at EI 250 and TMax unpushed at EI 400. And use D-76 1+1 (or Acufine if I need to push). Again these are personal setting and I tested to get there.