If you receive a "synchronization error" it would likely mean that your smtp client/script is sending the data before exim has sent it's welcome message. Â This is used to prevent script spammers from spamming you, as their scripts dont' usually wait for the welcome message.
Info: http://www.exim.org/exim-html-4.30/doc/html/FAQ_0.html#TOC86
Possible workaround for your exim.conf, top section:
smtp_enforce_sync = false