Jackmanii is a type III and blooms on new wood. You said you cut it back by half last summer after it had bloomed. Did you cut it back again this spring to within a couple of inches of the ground? If not, then that might explain why the blooms this year are only on the top portion of the vines. The lower stems would have been old wood from last year whereas the vines at the top are new wood and that is where type IIIs bloom--new wood. Either way, there is nothing wrong with your plant.

Actually, I did go out and cut them back this spring, only I cut all of the vines even with the ground instead of leaving them a couple of inches from the ground. I think I did what someone told me not to do, and that is don't prune all the way to the ground.