Hi Melissa,
What version of Survey123 app are you testing with now? Version 3.3 was just released last week.
As for the way it works, when you sign in you get an expiry token from the authenticating server if using IWA or ADFS, and as you are not on a Windows device (which IWA and ADFS are developed for) it can not automatically continue to renew your login based on the device sign in credentials. In Survey123, the app will cache you sign in details and use them when the device is offline or has no access to the authenticating server to display the signed in user in the app, therefore while the app is open you should still see the user signed in and the username can be used in the surveys fields.
However, the token that the server provided may expire during this time (depending on the server settings and length of expiry), meaning the user must login in again with valid credentials to obtain a new expiry token, this will happen when online and trying to use a feature that needs to request information from the server (download surveys, submit surveys etc).
Hope this helps, please keep in mind there are cases where users will always have to sign in again using IWA and AFDS due to token expiry, this is expected.
Phil.