I had a look at the video. The camera moves away from the overflow riser on the flush valve when the water is less than 1/4" from the top and the thing is still filling; a careful listen seems to suggest that the tank water level is rising higher than the top of the overflow riser and that water is overflowing into the riser before the valve shuts off. It's as if the water has become high enough to trigger a shutoff, but the valve takes a moment to respond, resulting in water down the overflow tube. Is that what's happening?
If cleaning the filter doesn't solve the groan or, more importantly, the overflow, then a new fill valve is in order. It's a very easy install -- water off, place bucket under bottom of fill valve, flush, disconnect water supply hose from bottom of fill valve, disconnect refill hose from fill valve and overflow riser, hand-unscrew mounting nut for fill valve, pull old valve out, unlock new Korky 528MP (or 528T), place in toilet, adjust valve height so water level mark on valve is 1/2" below top of overflow riser, twist to lock valve in place, tighten mounting nut (beveled side up), reattach refill tube, reattach supply line, turn on water, congratulate self.
If you installed the toilet yourself, this part is easy.
When you get your new fill valve, you want the 528MP [silver top] (which you will likely run with the refill all the way open: that's 40 percent refill, which is what the GMax valve is), or the 528T [blue top] (which is fixed at 40 percent refill). Don't let anyone sell you the white-top 528, because that won't refill your bowl enough (20% refill -- old industry standard). If/when you have this kind of problem with the 528 years from now, it can be fixed by cleaning the parts of the valve and if that doesn't work, by swapping out a little cap in the valve with a readily-avalable $3 part that contains the water-control diaphragm. Even easier than changing the whole valve.
Korky has a video on how to change the valve here:
Korky Installation Video Don't worry about the fact that they use a white-capped valve in the video; all the 528s are basically the same, except that some just have different refill ratios. (I did notice that the video says to turn off the water by turning the valve handle clockwise, which is correct, except that while saying this, they turn the handle counterclockwise. Doh!)
Anyway, good luck!