The back straightens up on the upward movement and remains straight upon landing. The landing impact is soft. Therefore the back pain is not due to impact. It would be a result of stretching the back muscles and the spine and the soft compression of the spinal discs.
Have someone run their fingers up and down the spine to feel if there is any protrusions or indentations of the spine, i.e., feel the spine to find out if the spine is curved outwardly or inwardly. Misalignment of the spinal discs and their compression would most likely be the cause of the back pain.
Stop jumping on the trampoline for awhile and do the following exercise.
Stand behind a dining chair. If the spine is concave, bend forward very slowly and then return to the standing position. If the spine is convex, bend backwards very slowly and then return to the standing position. Then have someone run their fingers up and down the spine again to feel if the protrusions or indentations are still there. Continue the chair exercise until there are no more protrusions or indentations to be felt.
Then find a minimal impact exercise like standing against a wall with both arms raised and watch TV during a commercial. If one can hold the arms up for the duration of the commercial, that means that one has been doing the arm raising exercise for about 00:01:30 to about 00:02:30 minutes. Men cannot keep their arms up in the air for more than 00:00:30 seconds but women can usually hold their arms up in the air for 00:01:00 to about 00:03:00 minutes.