Neither the current issue ammunition for US Forces, M193 (55-grain) and M855 (62-grain), does much tumbling anymore. This is an acknowledged problem, as often rounds are completely perforating their intended soft targets--instead of dumping the energy into them.
This was particularly noteworthy as one of the harsh lesson of the fighting in Somalia, the so-called "Black Hawk Down" incident. All too many of the Somalis were "walking-dead"--shot multiple times but not bled out yet, and able to continue returning fire. This was exacerbated by the disproportionate use of M855 ammo by the Rangers at the time.
Now, in Vietnam, in its original configuration, the M16-platform did truly overstabilize ("overrifled" would be more accurate) the 55-grain round; leading to truly devastating wounds. Sometimes, however, rounds would simply disintegrate in thin air (the centrifical force applied them surpassing the physical integrity of the bullet projectile). In this original format, it was a one-shot stopper <200 meters. Reports of horric founds and limbs blown completely off by 1 round, etc. This led the Vietnamese to actually file a Diplomatic appeal to the UN; which led to the redesign of the ballistic qualities of the M16/M193 platform to be more "humane".
Not that a current M193 or M855 round can't tumble given the correct conditions, rifle with correct rifling-twist, etc.; but in its current format it is not designed to tumble...
Sorry for the longwinded reply.