APA and Turabian/Chicago have different rules for capitalizing titles. Be sure that your article title is in sentence case, and Zotero can magically capitalize for Turabian/Chicago, and leave it sentence case for APA. Hover over the title, right-click and choose Transform text, then Sentence case. Only do this for English language items!
Be sure to double-check each citation as you pull it into Zotero. Check capitalization, but also make sure the information is captured in the correct field. While most of the databases (e.g. JStor) will pull the information in correctly, sometimes errors happen with the data entry. The best time to check it is as you're saving it, not right before you have to submit your paper!
Zotero is a great resource to save your citations and articles for future reference. You may find yourself wanting to reuse an article you read a year or so ago -- if you saved the information (and the PDF) in Zotero, you'll have it handy!