Try popping
smtpd_reject_unlisted_sender = yes
into your /etc/postfix/main.cf on a line of its own, restart postfix, and see how you go. I’ve not needed it myself, but the documentation points to this being the solution. When you test it, try doing it from an IP address that isn’t listed in my_networks as I suspect they will be permitted regardless.
http://www.postfix.org/postconf.5.html#smtpd_reject_unlisted_sender