Ok, if you know your original hive swarmed (perhaps you saw it happen?) then you could have just reduced the number of queen cells down to, say, three, and let them get on with it. All of the cells they would be raising would be swarm cells and intended to be queens from the outset. So no issues with being late starters.
Having removed all of the always-fed-as-queen cells made in conjunction with a swarm, you forced the bees to make emergency cells, instead. Sometimes this results in poorer quality queens if the bees struggle to find perfectly young larvae to turn into queens. As a rule, I think bees are smart enough to pick the proper-aged cells, but if you delayed your culling long enough perhaps they wouldn't have still had enough good choices.
All of the cells you saw initially were swarm cells, none were supercedure cells. Bees don't do those two things simultaneously. Placement on the frame doesn't determine which is which, though it sometimes gives a general indication. In supercedure there are usually less then five, sometimes only a one or two. In swarms there are usually dozens and they may be anywhere, and everywhere, in the colony.
Don't worry, you likely haven'tmessed things up irretrievably, even if you unknowingly interfered with the bees' plans, post swarm. Swarm cells make great queens, as do supercedure cells. I even like emergency cells when there are good options for the bees to chose from. Normally you don't need to add a queen when a hive swarms. Bees are really good at their jobs, and they can survive all our efforts to help them.
But keep an eye on things. if you only have a frame or two of bees, then they belong in a nuc box or queen castle for the time being. You can also reduce a normal-sized box with follower boards and foam panels.
Nancy