For years (over 10!) if I delete an email on my POP/SMTP accounts it does that. Only if I use an IMAP server does a delete sync up.
Not much has changed and in the case of POP3/SMTP we don't expect change.
I'm using a new iphone 5 and an iMac, all with the newest stuff. My verizon email account is not syncing when I delete emails. Anyone know why?