If you have tickets but you can't see them in the support manager. It could be two things:
1.) Permissions
Check if you've been assigned to the departments. Support > Staff > Your name (Edit) > Departments > Available departments are assigned to you. Check the Schedule to see if you are available to view the tickets at the moment in time.
2.) Database
If it's not the above then it's best to check the database, normally spam emails don't show up. To check this log into PHPMyAdmin.
Then go to Blesta database > support_tickets > click on status (to show all the status's) > Find open and change it to closed.
You can then go onto the support tab and then see the ticket.