Since we're guessing... I'll put my two cents worth in...
The "Tested for +P+" guns came out when many different agencies (fed and state) were using the "+P+" loads as something better than the old standby LHP+P that supposedly didn't work well in the FBI Miami shootout. The agencies were told to use the "+P+" loads in .357 magnum guns. Seeing that Smith & Wesson didn't have a .357 magnum J frame, they came up with the "Tested for +P+" Centennial for the ammo.
That's my story and I'm stickin' to sit.
p.s. I've shot a ton of the Federal 147gr +P+ in my .38 Special K frames with no ill effects whatsoever. My opinion is, they are not that hot of a load but VERY accurate.