What is the mechanism which causes the other side of the capacitor to rise to 10V?
My understanding is that the rise is caused by more electrons transferring from one side to the other. If you have five volts worth of electrons already collected on side B (using @Grumpy_Mike's example) and side A quickly goes from zero volts to five volts then five more volts worth of electrons passes from B to A. At that instant, side B is at five volts and side A reaches ten volts.