... so the email still appears in the Inbox on other devices

What other devices? Are those devices POP or IMAP clients?

My phone or other Windows based email clients that are all configured to IMAP. I had it working fine with eM Client and Outlook 2013 so it appears to be a setting with Thunderbird.

I tried creating other folders on my IMAP account to troubleshoot the issue. If I move an email on my Thunderbird client to an IMAP folder it shows locally but does not sync that change with the server.

One step at a time.

Wrt deleting messages, try to compact the folder you deleted the message from. It should then not be visible anymore on other IMAP clients.

Right-click folder - Compact

Thanks! That worked. Is there anyway to automate the Compact so I don't have to go through the manual process each time I delete something?

I don't think so. You might look for an add-on which places a button into the toolbar, to makes this a little more comfortable.

https://addons.mozilla.org/en-US/thunderbird/

Thanks again! I downloaded the Xpunge add-on and configured it to auto-compact every minute. That'll work for me.

I don't think compacting that frequently is a good idea.

Thunderbird ha a built-in mechanism to trigger compacting folders automatically. Check this article for more information.

http://kb.mozillazine.org/Compacting_folders

When your issue has been fixed, please mark this thread as 'solved'.
Thank you.