Been dabbling with an Osage self bow off and on for a few months.  Have it to a low brace and started to tiller.  

My question is, when should I flip the tips?  I don't want much curve, just a slight upward recurve to the unstrung profile of the bow.

Flip them now.

Anytime after floor tiller. The less wood you have the easier it is to bend.

Thank you.

I've noticed on a few posts that splinters sometimes lift when tips are being flipped.  (Although those were being flipped more than I want at this time.) Should I be overly concerned with that possibility?

I clamp the tip of the bow in the horm and heat it until gravity begins to take it down. This will usually do the job wthout cracking if you aren't flipping them too much. Osage reacts really well to heat.