I have sinewed after tillering out the bow and I have sinewed right after roughing out the shape and before I could get ANY bend while floor tillering. My opinion is to sinew as early as you like. Fact of the matter, you are going to be tillering that bow after the sinew has cured and why tiller it twice? No matter how good a job you do the first time, the sinew is going to change everything. As for getting the bow to pull into the correct reflex, you ought see how they pull more and more reflex as you take the wood down off the limbs! The current osage bow I am working on had no reflex whatsoever when the sinew dried (two months curing at room temp), but when I began to take belly wood off, there suddenly came three inches of reflex!
When I lay on the sinew, I take a fully wetted/glue-sodden bundle and lay it on a sheet of glass. I then use a fine tooth comb and lightly comb out the fibers so that they are all parallel and the bundle looks and behaves like a strip of ribbon. You do not need to get the teeth of the comb down into the bundle, but just rake it across the surface gently. Wet your fingers in more glue, pull the ribbon thru your gluey fingers and lay it down on the back of the bow. Get a little overlap on edges and sides of the ribbons, and when this sinewing job dries out there will be the prettiest bow back you ever saw! I rarely get any open cracks or furrows in the backs of my bows since I started using this technique. Oh, and have a large pan of hot, soapy water on hand along with three large dry towels! Messy business at best.
As usual, anything I post is open for arguement and I am willing to listen to anyone that can show me what I am doing wrong.