I can’t think of any reason why the PHP sessions on the server would be affected by the browser of a visitor in any way. Some reasons I can think of why the login sessions wouldn’t work on any particular device would be:
Your phone is configured to refuse or discard the cookies necessary for the sessions to be tied to the device.
Your login portal ties sessions to IP addresses, and the IP address of your phone changes very frequently (a fairly common problem especially on mobile networks).
In either case, I don’t know if it’s the case, and it’s up to you to identify and fix such issues.