Like the other device types and models, such as Yealink and Polycom, Cisco 8861 should not have a long reconfiguration period when signing out and signing in with a different user.

Check this CISCO article where it could be a custom config that RingCentral can implement to remove the reconfiguration in between shared lines login: https://community.cisco.com/t5/collaboration-applications/all-phones-restarted-while-login-with-extension-mobility/td-p/4459948