I've only made a few sinew backed bows and with each one I fully tillered and shot in the bow before adding the sinew. There are lots of options about this method also. In 2 cases I added 3 courses of sinew and waited a month between each course before adding the next. After the last I added a thin layer of TBIII, let it cure overnight then added the snake skin covering with TBIII and gave it another few weeks before stressing it. I wrote an article for PA Magazine, "The Story of Elkie"(vol. 15 issue 5, Oct/Nov 2007 ) about the process I used when making Elkie.
I believe the ancient Chinese waited 10 years or more before stressing their composite bows.