Hi @Anonymous ,
If you have created a rule in outlook to move emails automatically to Open Ticket Search folder, the situation you mentioned will appear.
Because of new email trigger monitors changes in the specified folder, if a new email moved to this folder, the flow will be triggered.
You could add filters to avoid the flow being triggered. For example, you could configure Importance to High. Then, only the message with high importance moved to Open Ticket Search folder, the flow will trigger.

Please refer to the online doc and get more details about Office 365 outlook connector:
https://docs.microsoft.com/en-gb/connectors/office365/
Besides, you could check each flow run history and see if each step of the flow runs as expected.
Best Regards,