It is not the printing process. You won't see the paper grain. If the prints look grainy it is the negative.
Hard to say if the grain in the negatives is "normal" without seeing the prints. But TMax 100 is virtually the finest grained film out there and should not give grainy prints at that magnification. Neopan 400 is significantly grainier than TMax 100, but a 5x7 enlargement should still be relatively fine grained. That being said, everyone has a different subjective definition of "grainy". Grain will always be most visible in featureless areas of relatively uniform density (cloudless skies etc) because there is no image detail to obscure it. HC-110 would not be the problem.
If small prints appear that grainy (again, hard to tell what that means without seeing), particularly with TMax 100, the only explanation I can think of, besides reticulation (which is pretty hard to pull off these days), is severe overdevelopment of the negatives. Gross overexposure in the camera would also contribute. Are the negatives particularly dense?
To rule out reticulation entirely, can you confirm when you developed the negatives the stop bath, fixer and wash water were all reasonably close to 20 degrees?