Oh, yes. Fixer removes undeveloped emulsion. So... if your firstfix was insufficient, you still have undeveloped emulsion left on your film. You can fix it again and that will come off. This is why I asked if your film looks milky. Milky may not be the right word to describe it although it's a common expression on APUG. There's no way Tmax can be completely fixed in 60 seconds.
If you are curious, take a small piece of undeveloped film, like the film leader you clipped off when loading film into the tank. Soak it in your fixer under normal light. If you keep pulling it out, you'll see it will progressively become clear. This is called "clearing test". You time how long it'll take for the film to become completely clear. Then multiply that time by 2 to get the proper fix time.
It's really hard to tell from scanned image but it looks murky to me. What I think should be white looks gray and grainy. I think that's undissolved (unfixed) stuff.