Garden mums, chyrsanthemums are easily fooled into thinking that every time the temperatures outside at night cool down just a little, it must be Fall, so they immediately want to set bud and flower. The problem is that just as fast as they set bud, it gets warm again and the flower buds never fully develop. It's true that some of them may try to bloom but those blossoms are not quite the same as the garden mums that bloom in the fall.
Garden mums are both temperature and day-length sensitive which means that when the day length is short (such as in the Fall) and the nighttime temperatures are cool, they want to bloom. July 4th (or soon after) is cut-back time so even though your mums have budded, it's not going to work out for you. Those mums need to be cut back, at least by 1/3, so that during these long, hot summer days they can grow back to the proper height, then bloom with a much better display of flowers this Fall, usually in September.
You really can't wait to do this since just after the longest day of the year, which was June 20th every day becomes shorter and believe it or not, your mums recognize this and within 2 weeks after the summer solstice, they start to internally form buds. The longer you wait, the shorter your mums will be and too short is not a good thing.
Dividing your mums at this time could be done however division is best done in mid-May while the mums are just popping up from underground.
Best advice for now is to simply go out and cut them back today. Fertilize with any general purpose fertilizer-they are all good.