Yes. For security, each account can have only one active app session at a time. When you sign in on a new phone, the session on the previous phone is closed automatically and the app takes you to the sign-in screen.
Your progress isn't lost: it's saved to your account and you'll see it on whichever device you sign in on.
The session on this website is separate: signing in to My account from a browser doesn't sign you out of the app. If your session keeps closing without you signing in on another device, change your password and write to us at [email protected].