I base info in the following three paragraphs on a 1986 article by Jim Sullivan of Armalite Div of Fairchild, "An Interesting Twist", in a special issue of SWAT magazine dedicated to the M16/AR-15.
The 55 gr fmj (M193) did not tumble through the air with the original 1 turn in 14" twist. It did yaw almost immediately, according to Jim Sullivan, upon entering flesh. With the 1:14 twist, it was just barely stabilized.
The twist was increased with the introduction of the M16A1 to 1 turn in 12". The bullet traveled slightly farther in to flesh before beginning to yaw.
It was this yawing that was called "tumbling", and many misinterpreted this to mean the bullet tumbled through the air. It did not.
Of course, the later faster twists, 1:7 for the A2, 1:9 for many AR-15's, and even 1:10, all stabilize M855 62 gr bullets (as well as M193 55 gr). However, in the slower M16A1's 1:12 twist the 62 gr was not stabilized.
This caused problems during the months leading up to Desert Storm. Some Nat Guard troops were still equipped with older A1's with the slow 1:12 twist, and M855 62gr bullets were not stabilized, would keyhole in targets. Their rifles had to be replaced with newer A2's.