When a ticket is routed to a group, the built-in Assign to first responder action gives the ticket to whichever team member replies first, even someone outside that group. A ticket cannot be assigned to someone outside its group, so the group is cleared and the ticket drops out of the group's queue.
Two automation actions keep the ticket with its group: assign to first responder from the assigned group, and assign to last responder from the assigned group. With either one, only replies from team members in the ticket's group count. If someone outside the group replies first, the ticket stays unassigned in the group's queue until a member of the group replies. If the ticket has no group, the first (or last) team member to reply is assigned, the same as the built-in actions.
Switching the default rule to the group
Every workspace starts with a rule called [Auto Assign] - Assign to first responder. It keeps using the built-in action until you change it.
Go to Admin Panel > Automation rules.
Click [Auto Assign] - Assign to first responder.
In the Then line, click assign to first responder.
Select Assign to first responder from the assigned group and click Continue.
Click Save changes.
The rule now reads: When a reply is added, if Assigned team member is Unassigned, then assign to first responder from the assigned group. The same two actions are available when you create a new rule with Add new rule.