I've tried 465 and 587 (both of which are enabled on my server), I've tried SSL and not; the user is enabled for both POP and IMAP both internally and externally... and they can pick up mail fine, but when they try to send, all I see is this:

Mar 9 16:19:33 benjamin postfix/smtpd[13832]: connect from m465536d0.tmodns.net[208.54.85.70]
Mar 9 16:19:34 benjamin postfix/smtpd[13832]: lost connection after UNKNOWN from m465536d0.tmodns.net[208.54.85.70]
Mar 9 16:19:34 benjamin postfix/smtpd[13832]: disconnect from m465536d0.tmodns.net[208.54.85.70]
M

Should I have them going out via the carrier's MX relay instead of my own server for some reason?

Same username and password in both the incoming and outgoing setups.