Tug driver reported the aircraft engines were at higher than idle power during pushback resulting in the aircraft moving forward and contacting the tug.

Narrative

Had to close the aft compartment door of the 777-200 manually aircraft mechanics said that captain seemed like he was trying to get out and on to the taxi way. Walk around was completed; tow bar inspection was completed. Got on the head set advised the captain walk around was complete; by pass pin and towbar was installed and they were clear for brake release. I was told to standby. We got clearance the brakes were released we were cleared to push tail east onto taxi way 1. I proceeded with the push out going tail east. As I was pushing I went in reverse to adjust the angle of the towbar; then proceeded with the push and gave the captain the all clear to start engines. The engines started and then out of nowhere it seemed the throttle went up as if they were preparing for take off and the plane started moving towards the pushback I called the captain told him to set brakes probably 3 times as the pushback was going under the plane the tires of the nose gear then collided with the back left tires of the pushback and prevented it from moving any further I again called and told the captain to set brakes and turn off the engines; he advised me to try and move the tractor so he could try and get back to the gate. At this point the engines were still on and I had told him I wouldn't be moving the pushback to call maintenance and he then turned the engines off. I proceeded to exit the pushback and that's when Person A proceeded to run out to check on my well being and that's pretty much it.Maintenance Control and the managers were there very quickly one of the union reps who was at another gate at the time ran over to check on me since I was still in the pushback.i exited the pushback and took a look at everything that happened.Suggestion: Making sure the pilots are doing there jobs properly and in a safe manner