(1) Johnson's wife probably was holding a Bible for him, but standing to his right, so he probably placed his closest hand (right) on the Bible, then raised his opposite hand.
(2) Illinois's current governor, Rauner, a Republican, did the exact same thing when getting sworn in last year. And there is no legal requirement to raise a particular hand.
http://www.bnd.com/living/liv-column...e17734655.html
P.S. Did you vote for Rauner? Or not vote at all? Because you don't strike me as someone who would usually vote for a Democrat.