That's how it worked then (for Romans), but it's not how it works now. So when the writer refers to Julius Caesar without any other qualifications, he refers to the adoptive father of Octavian. It's a minor nitpick though, hardly worth bringing up, but it is correct.

edit: as someone else observed, none of these were part of the late Roman Empire. Octavian and Nero lived in the early Roman Empire, and Caesar lived during the last years of the Republic.