When the servos drive to a new position the motors need a lot of current. This may cause drops in the supply voltage, especially when using standard AA or AAA batteries.
Most analog servos are very sensitive to changes in the suppy voltage. There is a comparator in it - it compares the voltage of its internal potentiometer (which tells the angle the Servo actually has moved to) against the integrated (lenghtended and flattened) steering pulses coming out of the DigiSpark.
When the supply voltage changes, the potentiometer voltage changes, too, but the inegrated voltage from the steering pulses keeps its value. So the comparator circut gets a wrong idea about the Servo's position and it starts to move erratically, causing more voltage drops.
So you could try to increase the capacitor (using serveral in parallel), or to move the servos at different times, and/or program a ramp so that they do not move to the targeted position as fast as they can, but a bit slower, so that the motors need less current .