syncing of iOS with dreamhost.com

https://help.dreamhost.com/hc/en-us/articles/216385537-How-to-set-up-email-on-an -iPhone

You can make the following changes in the Advanced section if you are experiencing any sync issues:

• You must set the IMAP Path Prefix to INBOX (all caps) for IMAP clients to work properly with DreamHost servers. Most desktop email clients work ok but instead show all the folders under the Inbox as sub folders rather than alongside it.
• If you are having trouble and suspect that you may have set something incorrectly, please refer to the Email Client Configurationarticle or contact DreamHost support.
• Recent versions of the iOS Mail client attempts to auto-detect whether the server supports POP3 or IMAP and select accordingly. To make the choice manually, give the Settings setup an incorrect email address, e.g., [your email address]bogus@[your domain]. The settings will not auto-detect, and you can then pick which protocol you want to use. Don't forget to fix your email address to [your email address]@[your domain].

If the quoted text from the article I linked does not assist you in this matter, I would look back to someone else over at dreamhost for more support. Even their documentation doesn't make any statement to refer to Apple on this matter. It sounds as though your email is acting like a POP3 account on your iPhone when it needs to act as an IMAP account.