The aircraft were at all relevant times broadcasting their position using ADSB. The controller had at least one screen displaying their positionx probably seve

The aircraft were at all relevant times broadcasting their position using ADSB. The controller had at least one screen displaying their positionx probably several. It may fuse multiple data sources. They may also have been able to see the Southwest aircraft, although maybe not clearly or only as lights. Despite this it can be difficult to judge the speed of an object at long distances under less than ideal circumstances and at night without a long observation period. So yeah they knew where they were but not the acceleration. It's also worth pointing out that the controller may have been in sudden stress due to realising the aircraft were too close, and so may have made a call that they already knew the answer to.