In a 15|10 is very possible to get a lot more time on the clock than started when playing fast. Also, the latter part of your post is lag or disconnects, neither of which can be impacted by your opponent as it regards your connection.
That said, discussions of cheating, potential cheating or cheat detection are not allowed on the general forums. If you would like to have that discussion, join the following group.
https://www.chess.com/club/cheating-forum
Chess.com takes cheating very seriously:
https://www.chess.com/article/view/chess-com-fair-play-and-cheat-detection
https://support.chess.com/customer/en/portal/articles/1444879-fair-play-on-chess-com-what-you-need-to-know
To report a suspected cheater to the Support team, please select Report Abuse under the Help menu, or use this link: https://support.chess.com/customer/portal/emails/new.
All reports are investigated, even if there is no immediate visible action.
A 15 min -10 does not turn his clock into a 21minute right? go and look and see the games I have played. I have seen them turn on the engine look how people cheat. I have seen them when the sight goes slow an blinks or they go off line.