Ok, you are wrong
From your link-
The thing passed in your story is the budget bill that allows them to
later pass a relief package via reconciliation.
It's not the actual package.
It can- though all bills for raising revenue must
start in the house.
(that said, courts tend to read that rule pretty narrowly.... and what the senate sometimes does is take some totally unrelated thing the house passed, gut it, and stick their own stuff in and pass THAT since it "originated" in the house)
Good example of that last thing here:
Continuing Appropriations Act, 2014 - Wikipedia