It should show up on all your devices.
you've tried refreshing the sent mail on your phone? (pull down on the screen)
what kind of mail is it? (google, aol, outlook, exchange, corporate, etc)
if you send mail on your phone, can you see it in the sent mail on your computer?
and vice-versa?
how is your phone configured?
there's 2 different ways mail severs work, POP and IMAP.
Pop is old, and doesn't hold onto things, if it downloads to one computer, it's gone off the server.
IMAP, is pretty much everything else these days. the mailboxes exist on the server, and get synced to your devices.
I'm not sure if the watch actually syncs with the phone, or syncs back directly to the server.