"WTF happened to constitutional Law?"
You're confusing Constitutional law with parliamentary procedure. Although it breaks with custom, there's hardly a violation of law in the Senate voting first on a bill, then passing it on to the House.
Remember, unless the House and Senate version of any bill are identical, they go to Conference Committee to have the differences negotiated anyway. Doubtless in this instance every effort will be made to get identical bills, but if buying the last handful of House votes necessary for passage involves adding in a few extra goodies to the House version, that's what will happen. And then the leaders' hand-picked conferees on the Conference Committee can make a match however they want.