Some valves (like the Fluidmasters I've used) pretty much are full on/full off. The Korky valves that are in most Totos taper on/off, so it could be barely on matching the loss. Unless the valve keeps going, and water goes over the overflow tube, it's almost never the fill valve, but a leak somewhere else.
I think that model is a 2-piece. When it was installed, did you check and tighten the big nut on the bottom of the tank? If it isn't the flapper valve, then it's most likely the seal between the tank and the flapper valve's seat assembly. You'll need a big pair of slip-joint pliers to tighten that nut. If you do take the tank off to check that, take the whole thing off, then lightly sand the porcelain around where the gasket goes and check for any bumps. But, usually, if it's leaking there, all it takes is a little snugging up of the nut.
If the chain length is too short or too long, or the flapper valve isn't clipped on properly, or the lever arm is pulling way to the side, that can keep the flapper from seating properly after a flush. A little judicious bending of the arm may be called for, or adjusting of the chain length. If you do try to bend it, you need to NOT apply pressure to the handle end, or you'll crack either the nut or the handle; IOW, use two hands and be careful to keep stress off the handle end.