Rainbow fish are egg layers, so certainly should not be in livebearers. They are Atherines, therefore not Cyprinids or Characins either, but we often have Rainbow questions in here. I've kept a few so have some of the other regulars.
Some of the Rainbows can grow quite large, 5"/120mm or more, but you rarely find specimens that size for sale. Given suitable conditions, they grow at a fair rate, neither lightning fast or terminally slowly.
In this particular case though, I believe the question is more to do with your catfish then the Rainbows! You need to know more about the disposition of your cat. An 8" catfish usually has a big mouth and likes to fill it!
I'll move it to Catfish and see what the people there say.