If it is Sunday, then B is Tweedledee.

But that means A is Tweedledum, who will not be telling the truth day after tomorrow, a contradiction.

Thus it is not Sunday, the only day on which Tweedledee could say what B did.

Thus A is Tweedledee and B is Tweedledum.

Today is the only day that Tweedledum could say what B did, Thursday.