Yes, you are basically right about light meters not reading tungsten light properly. You also have the issue of the warm tungsten light having less effect on the B&W film. The cumulative effect could be as much as 1 and 1/2 stops. Tmax's response to tungsten light is supposed to be very different from Tri-x. Some light meters are also better than others at compensating for the effect of warm light. the Zone VI spot meter, based on the Pentax digital is one of those.
You might also have the have the issue of non linear film response to shadows vs. highlights or midtones in tungsten. I think you should take a meter reading on an interior wall, in daylight, and another after dark using tungsten light. Bracket around the nighttime reading and find out how much you should adjust exposure. I find that using a light blue wall with Tri-x 320, I have to open up an additional 1 and a half stops compared to my daylight exposure.
Take care,
Tom