If you need to turn on the white light before the film is at least fixed for 50% of the fixing time, you can't use an alkaline fixer. The light exposes the rest of the unexposed silver halides before they've been fixed out and the carried-over developer, now in an alkaline environment and active again, goes to work on them. (BTW, if your indicator stop is still bright yellow, and mixed to the right strength, then it is still good.)
I had similar problems with TF-4 and a bit of a light leak near the fixer tray; got streaks and fogging till I found the light leak (a small crack in an otherwise light-tight window covering. I tend to use Ilford Rapid Fix these days anyway, just to be on the safe side.
However, I have (as a demonstration) done exactly what you are describing: After removing the film from the stop, I turned on the white light so everyone could see how the unfixed film looked, then proceeded to fix the film (in an acid fix) and watch it clear. It's kind of cool to do for those just learning B&W processing, but in real life I like to fix for 50% of the fixing time before turning on the white light.
Best,
Doremus