There is no need to simmer misua. In fact, I strongly advise against it because simmering will only release the starch from the noodles. If you let the misua cook in the hot broth with the heat off, the noodles will not turn soggy.
Three minutes is just about right to cook both the broccoli and the misua. While the misua won’t suffer if left in the hot broth for several minutes longer (even for as long as 10 minutes, so long as the heat is off), the broccoli will get overcooked. If you want to be sure that the broccoli is cooked just right according to your preference, eat a floret after three minutes. If you want it softer, cover the pan and leave the soup for another two to three minutes.