Hi there, just wanted to give you a big hug and tell you that this is absolutely normal at this age. A lot of it has to do with sleep consolidation, and the fact that their days and nights are getting straigthened out. Most 2-3 month olds experience this, and it does take some time to get it straightened out.. but it does straighten out (anywhere between 4-6 months of age, depending on child)
I always recommend at this age, to intervene and support with naps. Some parents will go in early, (30 min. mark) and when the stirring begins, placing hands on the arm and legs limbs to minimize the jolt. Also, take a look at room environment, a dark room helps with settling down and minimizing visual stimulation. For pacifier users, there's a post at the top from a consultation from Tracy, which was mentioned earlier.
There are partial awakenings (or jolts) every 10 mins. of an infants sleep cycle. Some infants will wake at the 10 min. mark.. some will wake at the 20 min.. and so on. Swaddling minimizes these jolts. Also keeping overtiredness and overstimulation at bay helps. I noticed you mentioned it's at the 30 min. mark.. here's what I reccommend: When he falls asleep, and is in deep sleep, stay with him, keeping your hands on his limbs.. yes I know this will be very boring, but the key is to help him get past the 20-30 min. mark of his sleep. You won't be doing this forever.. just for a few days, to help his body get used to sleeping past the partial awakenings/jolts. If he cries out, that's okay, just stay with him, calming him back into sleep (pat shush, leaning close to him and providing physical comfort-- you can do this by lowering the crib rail)
This isn't something that will disappear overnight, but it will improve with consistency, routine and also maturity on his part. I don't want to give you a timeline.. because he is young (I would look at his developmental age instead of his chronological age. So, if he was a month early, subtract the premie weeks from his chronological age)
Hang in there.. we're here for you and many of us have gone through this. and survived!
Take care,