If you did a walk away split and the bees already had CAPPED queen cells they will emerge sometime between 1 and 8 days after the split. She will be laying somewhere between 14 and 21 days after that. So we are talking between 15 and 29 days to a laying queen, with 21 days being most likely.
I think it's doubtful they were swarming if there were only 3 queen cells. Are they cells (with larvae) or are they just cups (with no larvae)? Assuming 3 queen cells with larvae I would assume they were superseding. Usually when they are swarming there are dozens of queen cells. Also, supersedure cells tend to be about the same age. Swarm cells tend to be staggered in age.http://www.bushfarms.com/beesfallacies.htm#swarmcellsonbottom