Tickets automatically re-opened when sent to alias of primary email address

I am new to Service Desk and have been trying to troubleshoot an ongoing issue that we have been having. Periodically when we try to close a ticket the ticket is automatically re-opened within minutes. I have finally seemed to identify a pattern. It seems that this occurs when someone outside our organization sends the original request to an alias of our primary ticket address. My assumption is that it relates to Service Desk Plus including the alias email address in the close notification. I called in to support and the agent's solution was to change the setting to not auto open a closed ticket when it is replied to but instead just add a comment to the ticket and email the tech. This option is not acceptable for us as it will be too likely that issues will get missed in our current environment. Has anyone else experienced this, and if so have a better solution?

Thanks,

John