Okay, so contrary to popular belief, impulses on nerve cells CAN go somewhat faster than normal. But it's not by hastening the info transfer, since it's impossible to surpass lightspeed. Instead, you could just make the information go through a shorter pathway, like giving it a shortcut.
This is doable because the impulse between different parts of the body are 'policed' by a kind of nerve cell called the glial cells. When certain connections happen a lot, these connections tend to be stronger, or even sometimes redirected so they can form shorter pathways; in contrast, connections that don't get stimulated a lot get pruned. This is why we remember and forget things—some connections grow stronger or shorter, while others get pruned or become longer.
Since Tohru had to hone his battle instincts to begin with (given how he deals with basically weapons slung and mobilized with a portable railgun), he relies mostly on muscle memory, but his own combat awareness would force him to still rely on cognitive work processed by the brain. Muscle memory are just connections to movement parts that get strengthened and shortened, making them doable and repeatable even without conscious control.
I assume that his ability means he just jumped these connections to their shortest possible paths, basically using his muscle memory entirely to move. Skipping the brain also means that all his motions are reflexive and respond the fastest to stimulus. Theoretically, he could surpass human limits of processing and motion this way.
Realistically, though, the difference from that limit would be negligible for the most part, because info travels at lightspeed, and the human body is too tiny for the distance that information traverses to matter much. But it's a cool ability, so I don't care. Just very happy to see him work around his demerits to unleash his true powers!