Hi – I can’t speak to Mendeley, but I use Zotero daily. I index my Zotero storage location using DEVONthink, and can with certainty that when I do something that causes Zotero to rename files, I have not experienced problems in DEVONthink due to the renaming process. In fact, it’s kind of impressive to watch in real time: with a window open on my smart group for references (discussed in another posting), if a file has already been indexed in Zotero and it gets renamed, the DEVONthink smart group will show the updated name after a second or two.
For this to work, the entire Zotero storage folder needs to be indexed by DEVONthink. If you index individual files, you will probably run into the problem discussed in the thread linked to above by @Blanc.
I wrote some explanations about how I’m using Zotero with DEVONthink in the pages associated with a software tool that I wrote to help DEVONthink-Zotero integration.