The simple answer is that autopilots are designed to fly the aircraft in the same way that a human pilot would.....only more accurately!
If you were climbing/ descending at 3500fpm you’d anticipate the level off earlier than if climbing/descending at 1000fpm or you’d risk exceeding g limits and it wouldn’t be a very smooth transition.
Autopilots, including ...
This looks like a proper setup for an autopilot controlled climb up to 5000 feet. One way to know for sure is to see what the Flight Director tells you. Does it seem reasonable and correct?
Also, prior to taking the runway, you should test the autopilot disconnects. Some of the more common ones are:
Can you overpower the autopilot manually.
The Control ...