Hello OP. Did you see/read the other thread you posted, about how to stop "hugging" the barrel? I responded but you did not.
When you "grab and sit" is going to depend on the horse. You will do so later on a push-style but will do so earlier on a free-runner. Either way, you do not want your horse to start the turn until your knee is AT or PAST the middle of the barrel. That will allow them to keep their hind end under them during the turn, and keep their momentum and smoothness.