How to provide external power supply for 8 servo motors?
The design is ok, the reason is that your power source is not able to provide enough current (as others have mentioned already). You need a 5V 16A power supply (it is a serious stuff, like a PC PSU, not a wall-wart) to provide full power for these servos in all circumstances. 

It is a good idea to add 2200uF/16V electrolityte capacitor to the power, or a 470uF/16V at each motor power in if there is a serious wiring distance.

It is also important to consider that you do need thick wires on the PSU rails.