When uninformed people bring up the subject of "tumbling" bullets, its a matter of defining what "tumbling" bullets are.
Bullets that tumble in the air as they travel are unstable and show poor accuracy.
Bullets that tumble on impact with tissue can be accurate and do severe tissue damage.
Most that tumble on impact are full metal jacket, or even lead like the old British .38/200.
Generally speaking, aside from the military FMJ in 5.56 that can tumble on impact, you do just about as well with a well-designed bullet created to be accurate in travel and then to expand uniformly and widely, with reasonably deep penetration.
Deliberately designing a bullet to tumble on impact isn't a simple matter. Most FMJs will just punch right on through tissue, creating little damage as they do.
For handgun ammunition it's not worth bothering.
Denis