Now it's all fine, it works. But I was actually planning to hide the sorting options, just leaving the "By begin date" as a default method of sorting pages. Are there any ways of doing so?
This way it's faster to do it via edit template `tags.tpl` and replace:
<input type="hidden" name="order" value="begin" />
Then you can stop `tags.first` part of plugin, leaving only `tagsort.pages.query`.
Also, if you have any ideas on another Tags issue, welcome! Here's the topic: http://www.cotonti.com/forums?m=posts&q=7730.
I'll check it later.