Hmm, if you're lifting under the proper lifting lugs/holes in the frame on some kind of adapter the rear should come up just fine.
Hard to tell from the picture but it looks like the jack is too far forward. But I may be imagining things.
Gotta say my lift adapter plate and bike lift combo was worth the rather high cost. Bike is rock solid and rises identically front/back, and no worries about fumbling it with some DIY lifting bracket slipping off or some such. I'm not that brave.
Though come to think of it, the Kern-Stabi plate I have is slightly tilted, ie the lifting holes in the back are not right up against the plate but some centimeters away. Also, the rear stopper (that makes sure the bike can't slide forward and off the lift) is not right under the holes, it's a little ways behind the holes so the lift itself is under the holes, not in front of them, not sure exactly how your adapter is done. But if the rear isn't coming up, it may be mounted too far forward.