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Time stands still - getting increment

It happened to me more than once here that, when me and opponent have only few secs on the clock and play very fast moves, his time like stands still, i.e. when I play move time passes (few tenths of the second) and doesn't go back, and when he plays a move he gets few tenths of a second back, like some kind of a increment, and as a result his time is like the same. Why is that? Our match ISN'T set with any increment (we play 3+0) and described situation happens only in last 4-5 secs of the match.
On Lichess, premoves take no time unlike on chess.com. So if his time isn't changing, he's probably premoving. If his time is actually going up without increment, then that's very strange and I have no idea.