Whatever world he is in, be it the real world or the Matrix or the MWAM, he had the ability to stop the sentinels. Possibly blow them up (or their bombs). It appears that the jack is in the same world as the Sentinals. So, is it a huge leap to assume he could move the jack? Not in my book.
With that said, I still think it is the Speak Machine that is jacking Neo into the Matrix.
Neo: "Agent Smith has grown beyond your control. You cannot stop him. But I can."
Speak Machine: "What if you fail?"
Neo: "I won't."
Speak Machine: "Okay, jack in and kill him. But I call dibs on his sunglasses."
Neo struggles to insert the jack, but cannot reach. "Umm...can you give me a hand here?"
Speak Machine: "You can't even put the jack in yourself? How are you going to kill Smith if you can't even do that? Hey, did you have problems putting the 'Jack' into Trinity. Ha! Ha!"
Neo: "Shut up and just put the thing in my head. I gotta kill Smith, go save Zion and make dinner before Trinity gets home."
Speak Machine: "Okay. Good luck. I find a little nutmeg added to a cookie recipe gives it a little kick...if you are interested."
Neo: "Really? Cause I've been meaning to-"
JACK GOES IN and Neo ends up in the Oracle's kitchen.
Oracle: "Get working on those cookies!"