For Outlook.com email, the most reliable way to keep email, calendar, and contacts in sync between a computer and an iPhone is to add the account on the iPhone as a Microsoft Exchange account, not IMAP or POP.
Try this:
- On the iPhone, open Settings > Apps > Mail > Mail Accounts.
- Select the existing account.
- Check whether the account has mail, contacts, and calendar sync options.
- If there is no calendar option, the account may have been added as IMAP. IMAP or POP setup syncs email only, not calendar or contacts.
- If sync is not working correctly, select Delete Account.
- Re-add the account using Microsoft Exchange:
- Go to Settings > Apps > Mail > Mail Accounts > Add Account
- Select Microsoft Exchange
- Enter the Outlook.com email address and tap Next
- Tap Sign In
- Enter the password
- Accept permissions if prompted
- Turn on the services to sync and tap Save
After that, test by deleting or moving a message on the computer and then checking the iPhone.
If deleted messages still remain on the iPhone, first check the mailbox in webmail. If the messages are gone there, the issue is with iPhone sync rather than the account itself. In that case, deleting and re-adding the account on the iPhone is the supported troubleshooting step.