Need clarification on Execute on Customer Reply in Workflows

Need clarification on Execute on Customer Reply in Workflows

We have implemented a workflow rule that will split responses to tickets closed older than 7 days to a new ticket but we are finding that in some situations this doesn't appear to be working properly.  A customer will respond, it will go into the original ticket, it will not re-open the original ticket and will not split off a new one.

In checking over the workflow the only thing that sticks out is the Execute on option.  Does Customer Reply only apply when the requester applies to the ticket or when anyone outside of the assigned agent responds?