Ramp agent reported a taxiway incursion while an observer in a tug was towing an aircraft on the airport surface to the hangar. When the driver received a clearance to hold short of a taxiway he then crept past the hold short line. The crossing aircraft had to slow down as they became unsure if the tug was going to stop.

Narrative

I was the observer in a tug. We were bringing Aircraft X from pad to hanger X; we had to go through [another route] due to an aircraft on the hanger service road. I called for my support team to wing walk us out of [that area] due to a widebody being on the blast spot; support did show up to wing walk. I make the initial call to the ground tower to reposition to hanger X; they tell to hold short; and we stop still inside [that area]. Then ground tells us to give way to company aircraft from right to left then proceed to hanger X; and I respond back to ground. I then tell my driver again the instructions that ground gave us to make sure he knew. Then the driver proceeds to pull up to the movement line and I thought the driver was going to stop but didn't and crossed the line before giving way. I immediately tell the driver to stop; what are you doing; we are giving way to the aircraft and I even pointed at the plane and then tell the driver we aren't supposed to cross that line yet. The driver doesn't say a single word back to me and then kept creeping slowly up to November Bravo taxiway. I had to yell stop since the driver wasn't stopping. At this point I'm waiting for the pilots or ground tower to yell at us on the radio for crossing the line when not supposed to. I believe it startled the pilots because they slowed down the closer they got. Our support team was confused as well cause the driver just caused a surface incident; they tried to call us on the radio; but I didn't hear due to focusing on listening to hear the ground tower and the aircraft to call us as into why we were that far over the line and close to the taxiway. Once arriving to hanger X support brought us in; and one of the support team ask what happened while the other support is talking to the driver. Both of the support team was very concerned about what happened and our safety. when I talked to the other support that talked to my driver and I ask the support team why the driver crossed the line and wasn't supposed to; the driver told him;' their was enough space'. It doesn't matter enough space or not; we're supposed to follow SOP and not cross a movement line til cleared from the ground tower. I felt very unsafe and in fear; because my driver has zero regard to safety.