The autotrim in Alt2 will only set the THS to "chasing" inputs if that input is held past the limits of elevator authority, otherwise it simply stays in the last position set when the FMC/autopilot kicked out. Letting the stick go in that situation will result in what you describe - i.e. the aircraft trimming itself back to it's stable position.
The only reason the autotrim moves to match pilot input is to give maximum control authority to a pilot in a significant upset without having to have his or her hands on both the sidestick and the trim-wheel. It follows that to have autotrim responding to sidestick inputs requires an emphatic stick movement held for some time.
Ok, I get it, he told the airplane to climb and it did. In this particular case Direct law would have been better than Alternate law since it wouldn't have trimmed him nose up, but if he hadn't held aft stick to the moon he wouldn't have been changing the trim either...
Somebody once said "it's hard to make anything foolproof because fools are so ingenious"......