When did you start the supplement and how soon after did the shaking start? If it was relatively soon after starting the supplement, then it definately sounds like a reaction to the supplement and I would stop it immediately.
If the shaking and twitching doesn't stop in a day or two, call your vet and set an appointment for them to look at him. If he gets worse, take him to the vet asap. 13 yrs old is sorta young for a cat having really stiff joints already, but not impossible since many factors affect this. However, makes me question if an underlying condition may be present and the supplement may have made it more prevalent.
Hi, Kattina, it sounds like a neurologic problem. Maybe it is a side-effect of the supplement. You might take him off it to see if the shakes and twitching stops. Also if it doesn't stop after a few days, you probably should have your Vet take a look at him. Hope he's better soon!