That is certainly not the type of statement (declaration of belief) I am likely to say is incorrect – just give my own view on the issue for comparison.
I am not a tiny bit Calvinist (rejecting all 5 of TULIP). But I disagree with a considerable portion of Arminianism as well. And what I read of God in the Bible doesn’t sound immutable (in the usual common language sense of the word) to me… which is not to say there isn’t some sense of the word which I would agree applies to God. Constant in His purpose, to be sure, unchanging in His love and integrity as well. But what I see described in the Bible is God who still has regrets and can change His mind about things. Back in the time of Calvin there was still this notion of absolute time which science has since abandoned. As a result there is no longer this black and white choice between being subject to time as we are and being without any kind of time at all. God can employ time all His own as He chooses.
I am reminded of a discussion on this forum not so long ago, in which this idea of God being simple was explained in a way that I agreed to, even though before this I as adamant in my refutation of that description.
That description of divine simplicity which I agreed with was “there is nothing which is not God which makes God be God.” But then… I would say this about God not being composite rather than being simple.