Finnish, it's true, my method is different.
When I first started making bows, I knew nothing about tillering.....and my bows were basically bent sticks. Then, after reading books, articles, and forums I made bows using the method you described. After a while, however, I began to see that I was not able to get good results with certain bow designs that placed a lot of stress on the wood. The short, double curve design is one of them....especially when trying to make reproductions.
The first stress that the bow has to endure is the drying process. Thinner pieces dry faster, and with less checking, than thicker pieces. That's why I rough out and floor tiller the bow when it's green. I low-brace the green bow and check for smooth bends in the limbs. I also remove remove snakey bends in the stave at this point, and align the tips. (I know that snakey bows work fine, but again, I'm making reproductions....and I haven't seen any snakey NA bows.) I start with the straightest staves I can find, in any case. After getting the limbs bending evenly at a low brace, the bow is thin and very close to final dimensions. It will dry out easily from this point onward.
I let the bow rest for a day after floor tillering & low-bracing, but not more than a week, before I steam bend the handle and limbs into the classic double curve shape. Some of the corrections from the previous bending/tillering may have undone themselves....and I take this time to re-correct those. A floor tillered bow is a lot less stressed during this process compared to a bow that is merely roughed out. The wood is easier to bend....and maintains the corrections better.
Then I let the bow dry out completely.
After the bow is dry, I use dry heat to make any further corrections, then apply sinew, let the sinew dry, and finish tillering.
I don't use a long string for tillering anymore, I use a slightly slack string...and I use it mainly to check on the draw weight of the bow @12". If I see a large flaw in the bending of the limbs, I'll make the correction at this point. Usually, at this stage, the bow is not pulling anywhere near the final design weight @12". Normally, bow makers will draw the bow back to a point where the design weight is reached, remove wood, and draw again to design weight, remove wood, etc. until the desired draw length is reached. I don't do this anymore. I use a chart to tell me if I'm on track to hit the draw weight at the final draw length. This places less stress on the wood, helps prevent hinges, and helps prevent problems with the handle reflex pulling out.
It takes some experience to get to know how to floor tiller the green stave so that it can be braced (when dry) and not be too weak.
