clock manipulation.

This may help you. Oddities stem from connection issues, along with lag issues from ones personal server.
https://support.chess.com/article/423-why-did-the-clock-times-suddenly-change-the-clocks-seem-broken

They gain 2 seconds each time they log out and quickly log back in.
No they don't.
But something do happen because I got a message saying they were sorry that some of my opponent break the fair game policy . So they notice something.

But something do happen because I got a message saying they were sorry that some of my opponent break the fair game policy . So they notice something.
That has to do with using disallowed resources. The clocks can't be modified as the server keeps the official clocks. Apparently there used to be a bug with the add time feature with friends but that isn't likely the case anyone ran into.
https://support.chess.com/article/779-what-happens-when-someone-is-caught-cheating

It may not add two seconds too their time. But it does interfere with you being able to move. Then they only haft to delay you to cause the problem. I was winning a game yesterday. The guy did it when we had ten seconds or so left. It may have been 7-8 seconds. But either way they won on time when they shouldn't have in my opinion. I wouldn't mention it if it didn't go on.

It's not your opponents. It's lag compensation and/or disconnects.
Shaving time off the clock or block of my moves, including algorithm, are not according to the rules of chess.
This program and website is geared to the winning of games for paying members and, or it's writers and owners.
To state otherwise, including Lagg, is a falsehood.
I will reiterate: This website should only be used as a training tool and practice.
Serious Chess is played else where.

Shaving time off the clock or block of my moves, including algorithm, are not according to the rules of chess.
This program and website is geared to the winning of games for paying members and, or it's writers and owners.
To state otherwise, including Lagg, is a falsehood.
I will reiterate: This website should only be used as a training tool and practice.
Serious Chess is played else where.
It works the same for premium and basic members.