On this website when it says it will cite a works for you, what format do they use? APA or MLA?
I'm guessing you are asking about eNotes, when you use the "Cite this source" button.
It looks to me like eNotes gives you the MLA citation. In MLA - the date of publication is sited at the end of the reference and in APA the date of publication comes just after the author.
"Grant Administrations - Introduction." Presidential Biographies. Ed. Kelle S. Sinsung. Gale Cengage, 2000. eNotes.com. 2006. 12 Jun, 2010 <http://www.enotes.com/presidential-biography/grant-administrations>
Because you are accessing references via eNotes, the second part of the citation is crediting that you found this on the internet. In that case the final date showing is going to be today - the day you accessed the material. Then it gives the url. I will say that this has been changed recently in the MLA handbook. Instead of putting the entire URL in at the end (which is often really long and ugly) MLA says you can now simply end each entry with a word of what kind of reference it is (Print, Web, Audio, etc.). For the above example you'd change it to:
"Grant Administrations - Introduction." Presidential Biographies. Ed. Kelle S. Sinsung. Gale Cengage, 2000. eNotes.com. 2006. 12 Jun, 2010. Web.
Of course, also realize when using pre-made citations, you need to reformat them on your works cited with hanging indents.
Difficult to know since you don't have the website posted. If you have been looking at a site like easybib.com, it will actually do either APA or MLA or several other formats. That is actually the beauty of the site, since you can choose whichever format you want.
No more having to run around consulting different books and trying to avoid the confusion between the two formats. The only problem arises when your instructor isn't familiar with the latest changes in MLA or APA format and counts your citations as wrong because they don't conform with their definition of the format.