All right, here's the solution we found.
1. In a table cot_config we search a required setting with a query:
WHERE `config_owner` = 'plug'
AND `config_cat` = 'tags'
2. Here we add a required field. If you need to sort pages by page_begin, just add begin (without page_).
3. Here we go! In the Tags plugin settings, find a dropdown menu with the options how to sort pages with the same tag. Choose Begin.
Voila! For this short manual, we send deepest thanks to Nastya Kizza. :)
p.s. Thx to Macik anyway!