I haven't used Tri-X for a while, but until recently I was shooting both T-Max 400 and Plus-X regularly. I have/am transitioning over to using T-Max 100 and T-Max 400 as my two films, but T-Max 400 is certainly most used.
Good negatives in both of Plus-X and T-Max 400 look a little bit different if all you are doing is inspecting them visually.
I've had pretty good success printing minimally exposed T-Max 400 negatives. My personal preference tends toward negatives with acceptable exposure, rather than generous exposure.
I expect the lab has a standard procedure for contacts that isn't fine tuned for each film. If you were doing your own contacts, you might very well adjust exposure slightly when you switched between them.
I've shown this a few times before. This is from a T-Max negative that is positively ghostly it looks so thin:
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