The Wolverine is not a pseudo anything to The Last Stand. All they've said is that The Wolverine takes place after it. That's all. They were just answering a question to when The Wolverine takes place, and they were basically saying after everything else that came before.
I'd be surprised if it referenced anything from TLS, except perhaps Wolvie missing Jean Grey. Of course, if TLS is retconned (and we don't know that it will) then (a) she may still be dead or (b) if she is revived, Logan may simply be missing her because he is away from her. Simple as
I don't expect The Wolverine to be replete with lines like 'Remember when we all had that big fight outside San Franciso and I had to kill Jean and Magneto lost his powers?'