Is ullage control a thing only engine startup? Would a rocket like the Saturn V or Falcon 9 leave an engine running for a second or two longer just for ullage control?
Yes, it is only done on engine startup. Remember, ullage is done so that liquid propellant is fed to the engines, instead of gas bubbles. When a tank is allowed to sit in microgravity for a significant amount of time, there is a risk of some of the gas bubbles in a partially-empty tank migrating to the tank's outlet at the bottom. An ullage burn at the end of engine firing would do nothing to stop this process. Instead, you do the ullage burn at the start of engine firing, to let the liquid in the tanks settle to the bottom.