Give us a little more background.
Was he there to work on the toilet? What was he asked to do and/or what did he say he did?
If this just started on its own, we can help you diagnose the toilet. Post a low-resolution photo of the tank contents with the lid off, if you can, or tell us the brand and model if you know it. New toilet? Old toilet?
These things are helpful but not essential.
Other questions: You say the water goes up and down, but the flapper (black thing) is shut tight. If you turn off the water to the toilet at the wall there, does the tank drain on its own? If so, you probably just need a new flapper, although it might be something much-less-likely like a crack in that riser, although that would probably not cause intermittent symptoms.
When the water is running, does it flow up over the top of the overflow riser (the vertical tube by the flush valve)? Or does it just fill to a level about an inch below that and then shut off? If the latter, then the fill valve (incoming water control) is doing what it is supposed to do.
In terms of the water hammer effect on shutoff, some fill valves are more likely to cause that than others. Again, is there a new fill valve in there? Is this a new toilet? Or is this an old toilet that just now started doing this?
My off-the-cuff guess is that all Mum needs is a new flapper, but give us some more detail and maybe we can focus the answer better.