and the other 3 powered by an external 5v power supply, tapping directly from the same battery that powers the arduino.
What is your battery? Hope it isn't four AA batterys. Also 5v is only .2v above the usual recomended 4.8v-6v servo supply voltages. Best to measure your power supply voltages while the servos are twitching to see what they actually are. Could be bad code, but the usual suspect is inadequate power.