On doweled shafting there are 2 ways the to orient the shaft on the bow with the grain lines horizontal. These will usually be the stiffer of the 4 sides. One side will be stiffer than the other, usually. Also, if I remember correctly, Art Butner told me that if possible place the stiff side of the top and bottom on the shelf however it seems rare to me that you will be able to put the stiff sides both against the stripe plate and the shelf so always place the stiff side against the bow(strike plate) and if possible against the shelf too.
The "stiff side" also relates to hardwood shoot shafts and cane. Generally that is the only spineing I do on hardwood shoots and cane.