Did you check the manufacturer information? I don't mean the stuff printed on the inside of the box, but the full information readily available on the web or even as hardcopy? When starting with a new film/developer combination, make sure that you get and read the manufacturer datasheets of both developer and film first - most of the manufacturers have datasheets available on the Web:
Tmax (and other T-grain films like Ilford Delta) have sensitizing dies incorporated into the emulsion that cannot be washed out very easily. If you don't follow processing instructions carefully, this sensitizing dye gives a purple/pink/magenta hue. According to Kodak, a slight hue doesn't influence printing, but if the color is stronger, it adds to base+fog density.
First of all, get Kodak datasheet F-32. Via the Web (see above) or from your photographic dealer. If you read the instructions carefully and follow them, you won't have any problems. In a few words, you need to dump your fixer earlier (because these emulsions exhaust them faster), agitate vigourously when fixing, wash a bit longer, and use Hypo Clearing Agent. As this is FAQ number one on the group, I'll just quote F-32:
"Fix at 65 to 75F (18C to 24C) for 3 to 5 minutes with vigorous agitation in KODAK Rapid Fixer. Be sure to agitate the film frequently during fixing.The Ilford datasheets for Delta films have similar instructions. If you have films with these residual dies in them, re-fixing followed by a long wash may help.
"Note: To keep fixing times as short as possible, we strongly recommend using KODAK Rapid Fixer. If you use another fixer, such as KODAK Fixer or KODAFIX solution, fix for 5 to 10 minutes or twice the time it takes for the film to clear. You can check the film for clearing after 3 minutes in KODAK Rapid Fixer or 5 minutes in KODAK Fixer or KODAFIX Solution.
"Important: Your fixer will be exhausted more rapidly with these films than with other films. If your negatives show a magenta (pink) stain after fixing, your fixer may be near exhaustion, or you may not have used a long enough time. If the stain is slight, it will not affect negative contrast or printing times. If pronounced and irregular over the film surface, refix the film in fresh fixer.
"Wash for 20 to 30 minutes in running water at 65F to 75F (18C to 24C) with a flow ratre that provides at least one complete change of water in 5 minutes. You can wash long rolls on the processing reel. To save time and conserve water, use KODAK Hypo Clearing Agent."