Platys are live bearers. The female usually carries for about 30 days, depending on water temp. The young will seek hiding places immediately since many fish, including the parents, will see them as lunch. The fry grow rapidly if fed well. Excellent starters are live baby brine shrimp and finely crushed plake foods.
If you have tank space elsewhere and want to grow them out, they can be moved to another tank as the sole occupants. A few will perish (just natures way of removing the least fit). Feed often and carefully do lots of partial water changes to maintain a pristine environment and they should do well for you.
Since the parents have beenhappy in the world you have them in, you are doing the right things and this care, although perhaps more of it, will serve the little ones well. I would also suggest keeping a log of everything about them and the world, date born, feeding times, food choices at each feeding, history of partial water changes, anything about them or their tank that you notice. That way, if you make any mistakes, you can look for what went wrong. Major point, do not get stressed about it. Enjoy watching them prosper.
Congratulations.
Charlie