>I would assume if the satellites orbit time is divisible by earths rotation time, it syncs up.

Right, that's how you get to SSO - sun-synchronous orbits. In terms of Starlink, that's Group 3 at 97.6° inclination. If the orbit is inclined just right for its altitude, it will be sun-synchronous and will appear over the same area at the same time every day. It will precess just right to keep up with the planet below. This is used by imaging sats to have consistent shadows and will be used by Starlink Group 3 to ensure additional peak time coverage.

Here's a plot of altitude vs. inclination, you can see Group 3 at 560km should be inclined to 97.6° to be SSO.