Gene,

           Did you allow sufficient time for the client where you did the deleting to sync to the server first, then make certain that the other client/device had done a sync to the server subsequent to that?

            Synchronization is not instantaneous, and occurs on timed cycles (at least most of the time), and if you've just deleted messages in one client/device, it has to sync those deletions to the server so it knows the messages need to be removed, then after that happens the other client/device has to do a sync so that it knows to remove them from itself.  I just had a client the other day who could not understand why Outlook on her PC was "so slow about catching up" to changes that had already occurred, whether that was incoming mail, deleted messages, etc., on her smartphone or tablet.  It was because the sync interval for Outlook was once every 30 minutes, which is an incredibly long time between checks if you want anything like the appearance of instantaneous change.  I never use longer than 10 minutes.
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Brian - Windows 10 Pro, 64-Bit, Version 2004, Build 19041  

Always remember that computers are just glorified light bulbs - they rarely fail in continuous use and usually go pop when turned off and on.

        ~ Technician with the username Computer Bloke, on Technibble.com