Does an ac servo motor experience high "inrush current" every time it moves after initial power up
This will come down to how quickly you try and move the motors in your servo loop, the inrush current is caused by the motor seeing full mains applied, and a phase error appearing across the phases as the rotor is stationary at that moment, while mains may be up to 90 degrees out of phase (maximum torque)

when you move a servo slower than its maximum tourque limit, the phase error is smaller, and thus the amount of current is smaller, your motors are in a control loop, meaning they never really stop while powered on, instead you will generally feel a vibration as the loop keeps correcting back to the desired point,

Because of this control loop, the maximum current is only dependent on how much torque you try and have it apply when moving to a new set point, for a constant load scenario this would mostly feed back to acceleration and top speed,

As for your controller, I would rather not go digging through the controllers datasheet, but if it has jerk correction, I would keep it set on the low side.