It easy to view each item in a bathroom as a separate entity: toilet, bathroom faucet, tub, and shower. But behind the walls and underneath the floors, each of these things are connected to one another through the plumbing, as well as to your main water line. Often times, water pressure problems are the root cause of your bathroom faucet leaking when the toilet is flushed.
Water pressure will naturally fluctuate, but when it begins to reach above 80 PSI, it creates a domino effect of problems in your bathroom. When you flush your toilet, water runs from the main line to refill the tank. When the toilet is full, it automatically closes the pipe between the water and the tank to prevent the toilet from overflowing. This shutdown is abrupt, forcing the water towards the gaskets. When the initial water pressure is too high, the water pushes past the gaskets, making its way into your bathroom faucet and causing it to leak.
Initially, the leaking stops once the water pressure dies down. But over time, this constant barrage of water wears your bathroom faucet out, resulting in a constant leak. While no one wants low water pressure in their bathroom, too high of pressure can actually damage your bathroom faucet and other fixtures.
The best thing to do when you notice these kinds of leaks in your bathroom is to call a licensed plumber. These problems may look easy to fix on the surface, but a competent plumber will be able to find the source of the leak and keep it from becoming a larger problem farther down the road.