CP treats the following parasites: Ich, velvet, brook, uronema.
Brook & uronema both have a direct lifecycle; meaning those parasites live, feed & reproduce right on the fish (no encysted stage). Therefore, CP at therapeutic strength should kill those in a matter of days.
Velvet trophonts can only remain on a fish for a maximum of 4 days, for ich it's 7 days. (This is according to all published studies.) Once the trophonts all drop off, the presence of therapeutic strength CP in the water shields the fish from reinfection. Since it will kill (or mortally damage) any free swimmers before they can attach to a fish.
So, technically on Day 8 you can transfer the fish into another QT. 10 days provides a little more buffer, 14 days is even better.
^^ Note: The above only applies if you are working with two QTs, 10 feet apart, and nothing gets transferred between them other than the fish. If you only have 1 QT, best to treat for 30 days and then do water changes/run carbon to remove the medication from the water.