When a First to Claim (FTC) group is connected to a leadflow source say from Zillow and that group receives a new lead in Follow Up Boss all members of that group will receive a push notification alert on their phones. The first member of the group who claims the lead (via the push notification) will be assigned that lead.
The purpose of a Fallback Action is If a lead is not claimed by the group within the time limit you can specify a fallback action to trigger another First To Claim Group, Round Robin Group, Pond, or individual team member to ensure no leads fall through the cracks.