When you log into a separate OS account on the same computer and then launch an Adobe app you are asked to sign-in again.
Use your Adobe ID and password to sign in the first time you launch any Adobe app for each OS account that you use on a single computer.
This is expected behavior because Adobe has enhanced the security around how apps store licensing information.
Note:
This use of your Adobe ID to use an application from different OS accounts on the same computer will not count as multiple activations against your Adobe ID as long as you are using the application from only one OS account at a time.