Servos jitter when powered by power module
Most servos use an analog signal (width of a pulse) for positioning.  Any perturbation in that signal will cause unexpected behavior.  Activating 48 servos simultaneously will likely indirectly or directly affect the analog signal.

The unexpected behavior might be mitigated through changes in software or hardware.  These mitigation efforts may include:

Staggering the servo changes so that only 1 servo moves at a time.
Perhaps less effective but worth trying, staggering the servo changes so only 1 servo starts moving at a time.  In this scenario more than 1 servos may be moving at a time.
Using a power supply which maintains the expected voltage even during events such as all servos starting simultaneously.

These are only 3 options to consider.  Many more exist but may not be pertinent to your situation.  More information is needed.