I wrote to the plugin developer (Dmitry) on this issue ( Обновление кеша ссылки - конфликтует с работой obsidian Sync · Issue #8 · derwish-pro/obsidian-consistent-attachments-and-links · GitHub). I have already talked to him on other issues. Therefore, I think, when he has time - he will explain the situation. As far as I can see, there is nothing in the settings that can cause this.
The plugin itself I really like and in Obsidian very much missing the functionality that has this plugin, for example - Move attachment with notes - #3 by davecan