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It's not the probability measure problem, as I am not worried about how to weigh different branches.
It's not the preferred basis problem as that is basically solved by decoherence.
I am asking why is the forward evolution of what is a detector at t_0 no longer a detector at t_1>t_0. The answer to this is that, by assumption, the forward-evolved detector is not what many worlds fans want to call a detector. So you need an additional assumption and this assumption is virtually equivalent to the measurement postulate in Copenhagen. I use virtually to mean "up to interpretation".
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Ihr Problem ist eben genau das. In jedem Zweig steht der Messwert fest. Der Detektor detektiert also nichts mehr, er wird immer mit Wahrscheinlichkeit 1 das Ergebnis in seinem Branch postulieren. So habe ich sie zumindest verstanden.