How long does it take for a servo to change rotation?
Normal servos don't provide any feedback. Their speed depends on the servo's specs and the load.

You could measure the time it takes to rotate a certain angle and use that to calculate the time, then add some safety margin. But if the load isn't constant, the times will be off.
You could change the position slowly, but that still doesn't guarantee that the servo will do what you told it to.

If you want to know servos's position, you need a servo that outputs it. There are servos that expose the signal from their internal potentiometer.



Adafruit sells them and has a useful guide about them.

You can also modify a normal servo yourself, by attaching a feedback wire to the potentiometer's wiper pin.