synchronization error

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.  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