Shimano shifter
 

Just attempted to install Ultrega 9600 right side shifter. It will ratchet up but not down unless I push in on the ratchet mechanism while flipping both levers together. Rear derailler seems to be adjusted properly. Everything is new. Drawings and instructions followed in detail. Anybody had a similar problem or suggested solution?

Considering there's no Ultegra 9600 you might want to check and let us know what you really have? Current generation Ultegra is 6700. 9600 is older gen Dura-ace

You do downshift a right STI lever by pushing both levers inboard.

shifters
 

Indeed it is 6700. Yes both levers together to downshift.