When people make predictions you can do the sums as bees have parameters and are dependent for growth on inputs to the hive.
You added 4 frame nuc, if there was 3 frames of brood they will hatch over the next 3 weeks. Yes you will have more bees, but enough for all the space you provided, maybe not.
The queen if the flow is good and there are enough bees to haul this flow in, will lay 2000 eggs per day. Her first day of laying will not hatch for 3 weeks.
So maybe the big expansion, everything going well, may not occur for 3-4 weeks.
Bees perform better slightly crowded rather than with excess space. Add extra space as they need it. if queen, flow and bees have not followed your script then the space is premature.