B737-400 CREW; AFTER PUSHBACK; RECEIVES A SALUTE AND RELEASE FROM GUIDANCE. PRIOR TO ACFT MOVEMENT; FLT CREW REALIZED THE TUG WAS STILL UNDER THE ACFT.

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WE WERE JUST PUSHED BACK AND GOT THE WAVE OFF AFTER STARTING THE ENGINES. THE MARSHALERS WERE IN A HURRY TO MARSHAL IN THE INBOUND ACFT AT GATE. IT MUST HAVE BEEN AT LEAST 10 TO 15 SECONDS AFTER THEY GAVE ME A WAVE OFF THAT I NOTICED THE TUG STILL UNDER US. IF I WOULD NOT HAVE SEEN THE TUG UNDER THE NOSE THERE WOULD HAVE BEEN A COLLISION WITH THE TUG. I DIDN'T SEE A FLAG ON THE TUG AS IT PULLED AWAY. SNA NEEDS TO EDUCATE THE PUSHBACK CREWS THAT A WAVE OFF MEANS IT IS SAFE FOR THE ACFT TO TAXI. SNA NEEDS MORE THAN ONE PUSHBACK CREW WORKING TWO JETS AT THE SAME TIME.CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: RPTR INDICATED THAT THE TRAINING OF THE RAMP PERSONNEL AND THE PROCS THAT ARE USED ARE NOT CONSISTENT. HE COMMENTED THAT IT APPEARS THAT SINCE THE COMPANY HAS OUTSOURCED THE RAMP OPS TO ANOTHER COMPANY; THE PROCS AND THE ATTENTION TO DETAIL HAS BECOME NONEXISTENT. HE ADDED HE WAS WORRIED THAT THE TRAINING OF THE PERSONNEL WAS POOR AT BEST AND IF THE FLT CREWS ARE NOT EXTRA VIGILANT; THAT AN ACCIDENT OR INCIDENT WILL PROBABLY OCCUR. THE RPTR MENTIONED THAT THE PROB EXISTS AT OTHER STATIONS; NOT JUST SNA; AND HE HAS BROUGHT IT TO THE COMPANY'S ATTENTION AND PASSED IT ALONG TO OTHER CREWS DURING THEIR TURNOVER AT THE GATE. RPTR ALSO EXPRESSED CONCERN ABOUT A FLT GETTING RUSHED AND THE FLT CREW NOT COMMUNICATING PROPERLY WITH THE GND CREW.