Duplication of indexed items

I index my Obsidian notes in DTP. I often need to keep both Obsidian and DTP open at the same time (sometimes on different machines), and that messes up with the note files by making several duplicate file entries.
Is there a better way to do this (assuming that Obsidian remains my editor of choice for now)?

Is the path of the duplicates identical?

Yes, it is. A number 2 is added after the file name.

A screenshot would be useful, thanks.

I deleted the duplicates manually. Let me try to share an example:

Original file name: file_name.md
Duplicate file name: file_name 2.md

So there were actually two copies in the filesystem, not only two references in DEVONthink? However, DEVONthink doesn’t use such suffixes (e.g. it uses filename copy, filename-1, filename-2 etc.). How are the files actually synchronized?

I will try and repeat this by opening both apps together.

The Obsidian notes folder is located on iCloud. DT also syncs its databases via iCloud.