DC Current is probably Battery current. Increasing that increases the power available to the controller, which will increase overheating problems if that's what is causing it.
The normal cause of vibrations is a motor/controller timing problem, which is usually caused by hall sensor signal problems.
They can overheat and begin failing to switch correctly; it's common enough. The way to fix this is to not overheat them, either by lowering power usage to the point where the motor can shed heat at least as fast as it is generating it, modifying the motor for better cooling (lots of threads about various ways to do that) or changing the system's properties (wheel size or motor winding (kV)) to match the actual speed vs power usage. (For instance, if you are spinning a motor slower than it's full speed while also using full power means it's wasting a lot of that power as heat inside it).
If it is resolved by increasing battery current available to the controller, then I don't know what is causing it, other than some strange controller firmware design. :/