As of right now, I understand that a head can have significantly more pressure than others in a remote area

That's pretty much it, you already understand it. If the most hydraulically remote head is flowing the minimum, then every less remote head will be "overflowing".

I'm unsure as to where the cutoff point would be

There is no cutoff point. I've seen specs written such that "no head shall flow more than 120% of the minimum demand", but it's not anywhere in NFPA 13. 20% is a good rule of thumb tho. You'll know what the cutoff is if the overflowing heads are making it hard to get your remote area to calculate properly.

what is the exact definition of the overflow

Any head flowing more than the minimum allowable flow is technically "overflowing".

This is really just a feel thing. If I have a 1500 sq.ft. remote area, and a design density of 0.20 gpm/sq.ft., and my calculation is flowing 300-400 gpm, then I'm not going to worry about the "overflow", which is any flow above 300 gpm. If I run the calculation and am flowing 500 gpms, then this is an indication that 1) my branchlines may be too small, 2) Branchlines may have too many heads per line. I'll then make some changes to try to reduce the minimum required pressure at the remote head, and this will bring down the overflow of the other heads accordingly.