Yes, when a bird moves its beak like that after you say a word to it, that is the parrot starting to mimic. It will often do it silently for a few days until it believes it can make the sound correctly audibly.
IF he was doing it completely on his own when you were not interacting (by saying "hello" to him) -- then I would believe it was him clearing his crop.
It sounds like he's getting bored after doing the same thing a time or two. Maybe start working on another trick at that point in time?
Keep the sessions short. 10 minutes would be the maximum I'd recommend and the 2-5 minute intervals are probably best.