What you are describing sounds like a disconnect issue. Your client got disconnected and for whatever reason didn't correctly assess that so the timer kept counting down. Eventually, the client reconnected and saw the correct times so it updated the clocks appropriately.
From your opponent's perspective, he made a move and you just sat there thinking for a very long time, though he may have seen that you were disconnected.
I don't know if anybody else has encountered this, but I found a bug with the timer in live Chess. I was playing a guy and was winning on time. He had about 7 seconds left and he made a move. Suddenly, our timers just switched. I was the one with a few seconds left now even though I was supposed to have 1:30 minutes, but he had 1:30 minutes (which was supposed to be my time). I ended up losing on time because of that. I'm playing on the Android mobile app if that makes a difference.