People ask the best questions on a psychology forum. ;)
Anyway, I have Type 1 Diabetes so we can relate.
Muscle twitches certainly are a symptom of Multiple Sclerosis, which we do have a 1/3 higher chance of developing.
I will assume as your Type 1, you substitute sugar for Aspartame? Or maybe Acesulfame potassium?
Both of which are known to cause muscle twitches and tremor when resting, which is often mistaken for Parkinsonian Resting Tremor.
Try cutting down on Aspartame or ACE K, and see if that helps.
If you're still concerned, you might want to talk to your Doctor. :)
MS often presents with many other symptoms such as stumbling, falling, tripping up, and general problems with balance, and since you didn't mention any of those, It's probably not MS.
If you find cutting down on Aspartame helps, you can choose another substitute sugar that's maltodextrin based, as long as they're recommened for diabetics. :)
EDIT: As Unknown said, stress can be a cause of muscle twitching and tremor, and diabetes can be stressful at times, so that's another possibility you may want to look into.