Just a reminder:
TAR 6 was also moved up by weeks to replace a failing show (Viva Laughlin after 2 episodes) back in 2004 (late November on Saturdays to mind-October on Tuesdays, IIRC).
TAR 9 premiered and aired a half-season in the 10pm timeslot (post Super Bowl and then concern about content, IIRC) in 2006 before returning to a earlier weeknight 8pm timeslot for the remainder of that seasons, and several seasons thereafter.
TAR's scheduling issue came because CBS half-expected one of its new fall series to run into trouble, but none of them did. Training Day was in ratings trouble from what was described in the Deadline Hollywood article from the time it premiered, so even if Bill Paxton hadn't died unexpectedly, renewal was unlikely, hence that show's move to Saturdays to burn off its remaining episodes.
But for the NCAA Tournament these next two weeks, TAR might have been moved up to next week (exactly what happened with season six after Viva Laughlin was cancelled way back when.) Expect of lot of TAR promos from now until March 30 or even ongoing since most folks were aware of the late April scheduling.