There should be pressure on your back, and if its painful you didnt do one of three things right:
1.) didnt warm up correctly
2.) twisted your back in an unnatural way, inconsistent with other jumps
3.) took off inside, which forced your top hand and arm back, jerking your back in a sudden motion.
This is assuming you dont have prior back problems, if you do, just stretching your back may hurt it. But generally, your back will have problems in the vault if there are sudden jerking motions. The vault is supposed to be fluid, and if your take off is smooth, followed by a huge-but flexible and smooth trail leg, you still shouldnt have problems. Just warm up a ton and take 2 or 3 short runs, increasing the intensity of your swing each time, before going back to a long run and really turning it up.
The greater the challenge, the more glorious the triumph