Should I include papers on a PhD application if I was not the primary author?
Yes, include it. It should be on your CV also. Tenth author can mean a lot or a little, but it is still an author. In my field, with your name, you would probably be listed near first, but if your family name was Waters, probably last.
But the important point is that you are an author of anything published under your name.
And certainly don't restrict it to primary author only, though you might want to highlight those in your CV.