Then in that case, we need to be consistent. Social security benefits also cut the taxes of those who receive the benefits. Or is it only a tax cut when the payment received appears on the tax return? If so, what is the relevance of the method of the payment distribution? How does that change the reality of what we should be calling it?
'What we shoul be calling it' is a function of linguistics and context, not a function of economics. Because you included that pesky word 'should', it's also a matter of linguistic philosophy.
The thing is, words carry feels, as a part of their meaning to people. People in general hear 'tax hike' and the sentiment delivered, the knowledge embedded in the phrase contains 'this means we will pay more or get less. We will be poorer for this'. The only group for whom that language is truthful would fit comfortably on piece of printer paper, perhaps even a notecard if you use a cramped hand and both sides.
It is a new tax, for the extremely wealthy, and a new benefit for pretty much everyone else.