The closer your monitor and mouse refresh rates are to each other, the more out of sync they will feel.
You an get away with a 125hz mouse on a 60hz monitor, because you almost always have a fresh(ish) mouse frame to display with every monitor frame. Furthermore, the end-to-end muse latency is consistently within what your mind and eyes consider "normal".
When you run a 125hz mouse with a 120~hz monitor, you can have serious issues.
If both devices are 100% in sync with eachother's rate (both at exactly 125hz for instance), then you will have a very consistent feel, but not necessarily a very responsive one, as synced rates are not the same as synced output times. Your mouse could be presenting a new frame 0.001ms before the monitor does, giving you a nice fresh frame all the time, which would be ideal, or you could have it presenting frames 7.999ms before the monitor frame, giving you a consistent lag that makes it feel like your cursor is dragging behind your mouse, rather than being directly coupled with it.
There is literally nothing you can do to force the mouse and monitor to sync outputs, so the changes of you getting a good result is low. Then there is the issue that almost no mice are 100% consistent on their rate, almost almost no monitors actually display at precisely 125hz. In the real world your "125hz" mouse is jumping around from 122-126hz, and your monitor is outputting at 199-121hz. Out the window goes all the consistency discussed above, and now you are constantly cycling through the entire spectrum between maximum and minimum sync, giving you a a laggy and jittery cursor.
To top things off, your mind is now twice as focused on movements, due to the consistently higher frame rate you are looking at now compared to when you were looking at a 60hz monitor. Flaws that you didn't notice then, you do notice now.
Ideally, you want your mouse to be running at, at least, a little over double your monitor output.