The M3 was developed to allow functioning with a variety of specialty loads - primary market I believe was law enforcement - tactical loads, tear gas loads, bean bag loads, etc.
Operates as a normal inertial system semi auto, but by unlocking the forearm, becomes a pump action shotgun. First shot only story is incorrect.
Now it does have a unique lockup and operation for a pump shotgun. You can manually cycle the forearm without pulling the trigger, which is different from a traditional pump action where when the hammer is cocked you must either pull the trigger or press the release button to cycle the action. This is normal for this shotgun - don't worry about it - the bolt lockup is different than what you think of for pumps.
A couple more unique features of the M3 are the recoil spring (remember, a pump-only shotgun does not have a recoil spring) will actually pull the forearm forward and close the action for you if you don't do so manually, and the bolt will lock back on empty (no more "click" after running the magazine dry as on a traditional pump). So you will know when you're empty immediately, you can throw a shell into the ejection port and hit the bolt release and have it loaded automatically for you ...
Nice shotguns, and a nice price. And good chance the H&K marked version also allows ghost loading without any modding (so you can load 7+1+1 if you want to) - mine does, but not quite as easily as my M1(haven't taken the time to determine quite what the differences are beyond the shifting of the recoil system forward of the bolt).