I read a source, a long time ago, that said an early form of the Japanese "Ninjutsu" originated earlier, during war-time in China, and was translated as "ninjitsu," but this art of espionage was never fully developed in China. The Japanese learned of this concept, refined it, perfected it, and made it famous (probably, most elements of the Japanese ninjutsu never existed in the original Chinese ninjitsu). I don't know exactly when they started using the modern term, but it was eventually labeled as "ninjutsu" since their language pronounces the term for "art" as "jutsu."
I believe that the "Jitsu" spelling (or better yet, pronunciation) is from Chinese influence, which is why some consider it an "older" version. As for the Japanese pronunciation and spelling, I believe it has always been "jutsu." Other experts might disagree with this, but then, what field ever has all of its experts agreeing on everything?