Yes, all autococker-based pumps have cup seals (except for ones with MQ valves, which I assume yours doesn't).
If it's only leaking when uncocked, the cupseal is probably not the problem.
What's happening is either
a) Your velocity adjuster is in too far or,
b) Your regulator is set too low or,
c) a combination of the two.
Try backing out the velocity adjuster at the rear of the gun and/or increasing the input pressure from the regulator and see if that doesn't help things.
At any rate, if the leak is coming down the barrel it's not the regulator's fault.
How fast a leak are we talking about? A slow hiss or is it rushing out?