I experience the same problem on both my Macs. The Esets_proxy process takes up to 100% op CPU usage and Safari is not responding for a while. Killling the esets_proxy process and restarting Safari is a workaround for me, but this is not the way it should be.
I contacted support and I was told it was fixed in 6.0.13. For sure it isn't!
Any updates about the support request ITUserSC?