One day in the refrigerator, 2 days out, the horn worms will slow down their growth. I use a temperature gun to avoid the colder areas on all my refrigerated feeders such as Butter Worms, Blue Bottle spikes, and Black Soldier Fly larvae.
I only do the slow down cycle after they reach 3/16 inch in diameter, and about 1-1/2 inch in length, younger horn worms don't handle the cold as well.
Regarding growing them in a cup, one of the main reasons for fatality is mis-moults. The cup and the moist food keep high humidity, and the screen gives them a hanging spot for molting. I have done tray raising which is easier than cups when doing several hundred worms, but i use the cups until the there is no more food, and the horn worms are too long for the cup. That is why I like the 32 ounce insect cup, and not the 24 ounce shorter cup, so the food is all eaten before the worms are too long.
CHEERS!
Nick