zoterobib is best for non database sources such as a website, or for database sources when the databases does not have the style you want to use.
It should be noted that many websites do not provide all the information that citation styles want, or the information is not on the page you view, but someplace else within the website. Your instructors do expect make an effort to see if you can find the missing citation information.
An easy way to see if all information was included is to look hit the Edit button under the citation that was generated. If there are any blanks, then you know that some of the information was not retrieved. Frequently this will be author, date published or publisher. Check the site to double check. If you find it you can just add while in edit mode and hit the Done button.
When the style you want is not available from a database, you can grab the DOI of your article from a database and paste it into zoterobib. How you grab the DOI from a database is very easy, but varies by database. Get step by step instructions below.
In EBSCO databases you can grab the the DOI at the bottom of each entry on your result list if it is available. Generally, DOIs will be available for scholarly articles published after 2011.
Alternatively you can grab it from the article page under DOI or from the citation option under most citation styles.