Yeah, Caesar was just Caesar, the emperors from the dynasty he founded continued to use his name, and then the emperors from following dynasties "adopted" his name as a title (https://en.wikipedia.org/wiki/Caesar_(title))
Julius Caesar has refused the title "imperator", for reasons of public image, even if de facto he had the same power as an "imperator", i.e. the power to give commands that must be obeyed by anyone else.
All his successors possessed the title of "imperator", so they are correctly referred as Roman "emperors".
Fun fact to whip out at parties but not applicable here