Keep in mind that the tutorial is VERY basic, it's more about getting a quick and usable result rather than a comprehensive rigging job.
The red vertices indicate deformable vertices, which usually aren't compatible with game engines. Although I don't mention it in the tutorial, when initializing physique, you should really change the "vertex-link assignment" to "rigid" in the initialization dialog.
No big deal though, you can still fix this using envelopes or manually typing in weights.
So, if you're not getting the results you want, then its time to start digging a little deeper. Try messing around with the envelopes in the forearm/hand area. Click on the little "+" sign next to the physique modifier and select "envelope" and start messing with the values.
And then from there, if you REALLY want to fine tune things, then start messing with the "type in weights" dialog box to manually assign weighting to each bone.