I have a lot of issues with the Cite feature in KOHA (the Cite in Zotero is fine). Personally, I don't like it as it is not correct at all! For example, the entire title of the item is not listed, there is no complete name of the author, and there is no italicizing for citation styles that use it. It also doesn't list which Chicago style it is using. Why is there both a Cite and Cite in Zotero? As a user, I would not scroll down to see the Cite in Zotero and just use the Cite feature which is listed first.
I'm assuming you're referring to the "Cite" menu item shown on the bibliographic detail page in the OPAC? There is no "Cite in Zotero" link in Koha code. My guess this is a customization to your system?