After becoming the One, Neo never entirely breaks his connection to the Matrix.
He wirelessly communicates to the Sentinels through the Matrix to simply shut down. Similarly, his sight regarding machines is due to him being connected to the Matrix that basically transmits his position relative to the machines. By interpreting the code, he develops a limited concept of sight.
and...
Yes, he "touched the Source" ie was connected to the Machine Maneframe while in the Architects chamber, located there.
He was the first human to ever leave it again the way he did, it had unintended consequences as his mind was further removed from his body to be uploaded to it.
On being replaced to his body, he retained...for the lack of a better term, a wifi connection to the Source, and anything in it in his location. Notice he only ever shows this ability near a Hovercraft (the Hammer was still close by when the Nezzy went up, Logos out in the no mans land) or the Machine city itself, near broadcasting equipment.
My point is that an organic human brain has no wireless capacity whatsoever. Neo can't communicate with ANYTHING wirelessly. If the movies had established that there were some telepathic people, then I could buy it, but there's NOTHING in the movies to indicate that anyone could use their mind to affect other things without the use of technology. Given that Neo had no access to such technology at the time, his ability to stop the sentinels makes no sense.
He still had the implants. We don't know what they all can and cannot do. There may have been some connection with them to the matrix.
Also, I have my own theory on what the whole thing was really about. It all comes down to the dangerous game the Oracle played and is referred to by the Architect when he noted the difference between this "ONE" and the previous "ONEs."