I'm no expert by far, but have had issues with this before.
IMAP should allow your iPhone to remove messages from the server.
But have you made sure both the iPhone and Outlook are connecting via IMAP?
If your iPhone does remove the messages from the server, but your computer is using POP, then the computer may download the email before it is removed form the server by your iPhone.
This was my issue, that my computer had already downloaded the message, and POP does not check later if it is deleted.
If you delete a message from Outlook does it disappear on the iPhone?
Alternativly you may need to check the email server settings.
Who is your email provider?
They may be able to check if IMAP allows you to remove emails.
Thank you for your reply. Actually I'm using hmailserver with pop but on iphone I set imap as pop was working in a weird way and bring back old emails in a crazy way. I tried imap and It was working better but the only issue is with deleting on server.
I'll be travelling for 2 weeks and can't imagine the amount of emails I need to deal with once I'm back if I don't find a fix.