There are many people who experience something like this without it being associated with seizures. However, if you any type of seizure disorder, you may be more likely to have them during these times. This could also be the only time you have them.
I would discuss the specifics with your doctor. If s/he thinks it could be seizure activity, you can be referred to a neurologist for an EEG. You could also request this if you are concerned about it and don't feel that the doctor's explanation was good enough.
This is commonly known as a myoclonic jerk, and is not dangerous, and is not any kind of fit or seiaure. It is very common, especially when falling asleep, or in the early very light stages of sleep. It is sometimes accomapied by a sensation of falling, just prior to the jerk. It is usually not a problem when associated, as you have said, with falling asleep. If you are concerned, discuss it with your doctor at your next checkup.