I don't think the rats will just vanish with the food, they keep searching the property. Squirrels don't just feed, they hide the surplus food for winter months. Not just in one place either, but all over. Regardless of whether the OP caused the problem, or not (likely always had the rats, since he already had the squirrels). He needs to get busy before it starts getting cold outside, and shelter becomes a higher priority than food for the rats.
It took less than two months from my initial sightings, until they were doing property damage. Not sure if I ever mentioned it, but the cat feeder lived next door for over 5 years, and this was the first time I had a rodent problem, ever.
Feeding squirrel for a month, and 20-30 rats? I live in the middle of town, and that many rats is an infestation to me. Perhaps out on the farm, it's not a big deal. Numbers might be a little off, but believe the females can pop out 8-10 babies, every 3 months. They can start as young as 6 weeks... They already have food, whether you continue to provide for them or not. Suppose it depends on where you live, but for me, I knew I had to take control quickly.