Trigger on Case not getting invoked/fired on Email-to-case creation

Hi Trailblazers

I have created a Apex Trigger on Case object which is supposed to be fired on "Before Insert" or "Before Update". When I create the case manually, it gets fired and executed successfully. But nothing happens when case is created via Email to case functionality.

I have also tried adding "After Insert" and "After Update" condition just for sake of checking and got same result.

Can anyone please suggest something one this, is this expected that triggers don't consider cases created via email-to-case as inserts or this can be fixed or implemented in some other way.

Thanks

Rishi