They swarm for a number of reasons. Sometime it is the pests, wild animals bothering the hives, management (feeding), reproduction, etc. As beekeepers, we're suppose to do swarm management before there is even the thought of a reproductive swarm. This is done 2 months ahead of the yearly flow. So yes, even with a single hive and a super on, they will soon run out of room when the main flow hits. It is not how many boxes they have drawn out but rather how crowded they are at the time of the flow.
And when you feed them on a flow this is even worse. Because soon the brood nest will all be back filled. Then they will make QCs ready to swarm thinking that no more room to grow further. One box and one super that is it; time to find another bigger place to live. For every growing nuc hive this season, I installed 2 deep nucs in between the honey super(s) and the bottom brood nest with drawn comb. No issue with swarming!
Next season, have all your drawn comb ready and install the supers as soon as you see them flying after the winter. Over here it is early Jan. usually. By mid-Feb. we can make our 2nd batch of new queens. So know your flow, your management style, and your bee's behaviors as each year is different from the last. We have cooler weather than last year so I adjust my management differently this season.