Is there a time-cheat?

Please, just accept your mistake. Thanks

This would be true if the clocks you see are purely under the control of the server.  They're not.

The clocks you see are controlled by your own computer, then updated with information from the server.  There's no lag between your computer and itself, so your opponent's clock continues to count down normally after you make your move and until you receive your opponent's move.  At that point, your computer updates your opponent's clock.  If there is little to no lag between your computer and the server and/or opponent's computer, then these updates are minimal and likely unnoticeable.  If the lag is large, then the updates become much larger.

A simplified example:

Your opponent has 2 minutes left when you make your move.

It takes 30 seconds for the move to make it to the server, and another 30 seconds to get to your opponent's computer.  At this time, your opponent's clock *on your computer* shows 1 minute left, but your opponent's clock *on your opponent's computer* still shows 2 minutes left.  They make a move relatively quickly, or have a pre-move set up.  It then takes another minute for their move to make it to your computer.

At this time, it looks to you like your opponent has run out of time.  However, when your opponent's move finally arrives, it also contains information about how long your opponent actually took, and their clock then jumps back up to reflect that new information, bringing it back up to close to 2 minutes remaining.

That is exactly what is happening and the site provides an article explaining it. @omnipaul explained it very well also.

The simple fact is the clocks will always adjust upwards some from where there were just before the move is received by the client. The client may not show it, since most of the time, on a low latency non-nondisconnecting connection, the time adjustments are in seconds or milliseconds. In a high latency connection, or one where there are disconnects, you can see larger jumps. 

There transit time between the server and your client will never be counted against your opponent, but their clock on your side starts decreasing as soon as your move is made and until you receive their move. Since it isn't counted against their clock, the time has to be added back.

That doesn't explain the blitz opponent who had about 1.8 seconds left and managed to make 15 moves and win the game using about 1.1 seconds, does it? This was several years ago but it's happened since although not as extreme.

I don't understand pre-move, have never used it and don't know how to access it but it couldn't possibly have been premove since I started making very random moves indeed. It was a connected engine, wasn't it.

That's impossible, since premoving takes 0.1s off your clock. You say you don't understand premoves, but you also say that can't be it? That's illogical.

Actually you're being illogical. I knew about the 0.1 second thing, therefore it must have been an engine hooked up. I don't understand pre-move in the sense that I've no idea how to use them or, for that matter, what they are.

The archive of the game would show exactly how much time was used. If it was premoves, it wouldn't matter what moves you made because your opponent had already moved their piece. The only way to disrupt a premove is to make a totally unexpected capture since your opponent wouldn't be thinking of that in most cases.

oh that makes sense!

It doesn't matter, you could have an engine hooked up and it would still consume 0.1s, as the archive would show.

https://www.chess.com/club/dora-my-little-pony-thomas-train-choo-choo-and-humty-dupty-fan-clubs

Choosing the premmove option allows you to make next moves in anticipation before your opponent has made his move.

This way, your selected premove will play immediately after you opponent's, which spares you a lot of time. 

To be used carefully, as you might make a premove that screws up your game if your opponent's move was an unexpected one.

It’s a cheat

Time manipulation using lag the server internet chess is destroyed by cheaters using all kind of cheats