When doing ROCK STAR FAME you must get 1k likes AND 1k rates while running Rock stars.
Any rates or likes earned prior to starting the first Rock star, in between Rock stars or after Rock stars expire will not count towards the achievement.
It is best to note how many Rates and Likes you have prior to activating the first Rock Star so you can do the math later to know how close you are.
You can run any other ability bling along with the Rock stars and as many Rock Stars as it takes to get the achievement.