Zotero and Ebsco can work together provided you remember one basic tip: If you have the standalone version of the software, this version must be closed in order for the Zotero/Firefox add to work properly.
There are a few ways to save information to Zotero from EBSCOhost:
Click the document icon to save this item in Zotero.
From the open result or from the folder, click Export. The Export Manager panel appears.
If you are in the folder, Remove these items from folder after saving appears. Indicate whether you want to empty the folder of all items after saving your file.
Save citations to a file formatted for: select one of the following:
Direct Export in RIS Format (e.g. CITAVI, EndNote, ProCite, Reference Manager, Zotero) - includes those fields supported by reference managers that utilize Research Information Systems (RIS) format for bibliographic management.
Click Save. Zotero should automatically open. Sometimes Zotero is able to download both the citation and the pdf of the article from a bibliographic database. However, Zotero does not seem to recognize the pdf's in Ebscohost. You will need to download the article pdf separately.