The tops of my Eastons tilts toward the rider. Should allow your palm to rest there at a comfortable angle that it obviously would not be at if the flat part was horizontal.

 

You basically need to experiment by doing both, tilting the bars and repositioning the brifters.

 

The bars are intended to be comfortable. Ignore the brifters for a few minutes and get the rotation of the bars set to where you are comfortable on the tops and on the drops. Once it's set, then position the brifters to make them comfortable (if necessary).

 

The bars are intended to be comfortable. Ignore the brifters for a few minutes and get the rotation of the bars set to where you are comfortable on the tops and on the drops. Once it's set, then position the brifters to make them comfortable (if necessary).

Exactly the right procedure. And I'll add a terminology note, since you'lll generally get better answers sooner if you use the terms in the way that people are accustomed to using them. "Anatomic" bars does not generally refer to the flattened "wing" shape on the top section, but to bars that have a section of the drops that is straight, rather than uniformly curved. Anatomic bars (with various bends) are more common now, so the confusion is understandable.

Anatomic bar:

"Conventional" bar