| | Re: on my time
It's very difficult to answer this question as you haven't given the context and, as always, interpretation of meaning is always affected by context.
However, the expression "to do something on someone else's time" means to do something for personal reasons when you should be working - ie when someone else is paying for your time.
For example, if you spend an hour at work writing personal emails rather than getting on with your job, then you are answering your emails "on the company's time".
To invent a context for your sentence, it might be eg in a factory where the workers on a production line are doing a fairly routine mechanical job, but there is background music playing to make things less boring. One of the workers starts dancing to the music and after a minute all of them have stopped working and joined in. At that moment the boss (the factory owner) arrives and says angrily : Stop dancing on my time!