The sync password never leaves this device. It is what encrypts the copy kept in the repository, so it must be the same on every device that shares it; the token only opens the repository. It is asked for once: afterwards the vault opens with the phone screen lock, an app code, or this password - your choice, under Unlock with.

To jump back to the app you came from, use Android's own gesture: swipe along the bottom bar, or tap the recent-apps button twice. After a copy the vault stays open for 2 minutes in the background, time to paste the username and come back for the password.