Thanks. That fixed templates issue.

The import code for style.css was indeed missing in the templates update function. I attached an updated admindoupdateset.php that fix this problem to this post.

However, I can't reproduce the problem with the site_* templates. They just update fine here. Perhaps you have the caching system enabled? In this case you most likely saw a previously cached version of your site. I highly recommend keeping the cache disabled while working on the layout.
   admindoupdateset.zip

I will look into it

I did that but it only imports half of files from database. Not site_ files or style.css.

Sounds like you have the file cache enabled and edited the cached CSS file.

The original CSS as well the templates are all stored in the database. If you like to edit them with an external editor, you need to export the data to the /templates directory:
Templates => Import/Export => Export Template Set to HTML/PHP files

Once you are finished, upload the files back to the /templates directory and then import or update the template set.