Rated 5 out of 5 stars
This is good add-on. But I found bug?:
I have website in Work tab. After editing website in Google and syncronization, Add-On deletes it from Work Tab and fills Private Tab. Is it normal behaviour?
That's expected (though unintuitive) behavior. Google has types/labels for websites while vanilla Thunderbird just has a work and home website. To allow synchronizing all different website types/labels gContactSync adds a drop-down to the TB work and home website fields and syncs the first two websites of any types with these fields.
The work tab has the second website field, so if you sync to Google it is added as the first and only website. If you sync back from Google Thunderbird syncs the first website with the home/private field and removes it from work.