No: let them continue to brine in it. You may be better off putting them in ziploc-type bags so that more of the brine is in contact with the meat.
Now it's sit and wait for a week. If they throw off some liquid brine am I supposed to drain it off?
Are you planning on rinsing them before you hang them? I think the Ruhlman recipe calls for that; I don't know about the others. I did, anyway, and I think it was a good idea.
Rinsed, dried and hanging in 43% RH & 55˚!