Subject to one possibility (see below), I think you are right: the date of first contact rule only applies if none of the other “treated as made” rules are satisfied. You cannot treat the claim of 31/1/ as having been made on 19/1, and then treat it again as made on 21/12
The claim was not made within a month of 21/12 (assuming 21/12 was the date of the JSA [b:5e4ba6351b]claim[/b:5e4ba6351b]). So that doesn’t apply. So the first contact rule does – claim treated as made on 19 Januaryt.
Now that possibility I mentioned …. any danger you could say there was a telephone claim on 19 January, or is your LA not doing that yet? If so, there was a claim within a month of 21/12 and that would be satisfied after all.
But failing that, I agree with what you have said up to now.