My research showed the rudder was first turned to the left ("starboard helm" in 1912) and then, as Murdoch "ported around" the iceberg, it was turned back to the right ("port helm" in 1912). There are no additional helm orders recorded in the testimony. However, there is plenty of evidence that the ship's engines were re-stared and the ship steamed for between 10 and 20 minutes following the iceberg incident. It is highly unlikely that Titanic steamed in a circle, so from this it can be inferred that an order to "center up" was given, probably by Murdoch who still was the officer of the deck. Quartermaster Hitchens claimed he was kept at the ship's helm until approximately 12:25 am, almost 45 minutes after the iceberg. It is unlikely he would have been kept at the wheel unless the ship were moving during that period of time.
Titanic did have two steering engines, both geared to the ship's steering quadrant. The design of this type of steering makes it unlikely (to downright impossible) that any force other than the steering engines would have centered the rudder. As mentioned, only one engine would have been working at the time of the accident, the other would have been in reserve.
Based on all of this, I'm betting that Hitchens straighted the rudder while steering a course of about "north 10 east" from 11:50 pm to 12:20 am.
-- David G. Brown