If you’re using and sharing a single email account from multiple separate devices, and the mail messages to be deleted are stored on the same shared mail server, then you’re asking about two mail clients to have different and diverging views of what’s actually stored in the server. One real—the client that views the now-deleted message—and one fictional—the mail client that views a cached copy of a now-ghost message...
if you’re seeing a case where one client is not connecting to the mail server and not keeping current (and iOS and iPadOS will both indicate connectivity problems, but that indication might not be obvious), then that client has bad settings, and you’re seeing cached data.
Each mail client has two sets of settings for the mail server. One set for reading and receiving messages via POP or IMAP—and one set for sending messages via SMTP or ESMTP. Both have a host name, credentials, an IP port, and related details, and the two can be and in parts always are different. Both sets of settings have to be correct, too.
If you can’t send or receive emails on your iPhone, iPad, or iPod touch - Apple Support
Now if you’re using POP, POP by default downloads the mail messages. Use IMAP. IMAP doesn't download the messages. IMAP leaves the messages on the server. With POP, the first client that finds the message downloads it and deletes it off the server, and the other clients find... nothing, ISPs like POP, as it offloads the server storage.