I agree that it looks like mite damage, not aster yellows. Here is a really great website from OSU that compares the two. The only way to get a definitive answer is to take in or mail in a sample into the lab at MSU. Here's a link to the lab's website. 

If you are concerned about the mites or infection spreading, you can remove (at very least) the flowers and stems or the entire plants. I would put them in the city compost/yard debris pickup (not in your home compost). 

If you send a sample to the lab, you might as well wait until you get results. However, if you don't want to send a sample to the lab and your are concerned about infecting your garden overall, you can choose to assume the worst and dispose of the plants. I had a coneflower last year show signs of mites and chose to err on the side of caution and remove the plant.