Guess there are different ways to team pen.
In ranch rodeos in TX, they have cattle behind a line, one cowboy goes in there and sorts their number, generally three cattle and pushes them out and that cowboy and two others chase them around and into a pen on the other side.
Barns that offer team penning around here have also team sorting and those are different, generally two riders go into a pen and run those with a number out.
You can see all kinds of riding there, but most that is for time in competition and tends to be kind of everything goes, rarely anyone has the time to go easy and move cattle without stirring them up, something you don"t want working cattle, makes working them next time more difficult, hard on cattle and just poor cattle handling.