Ship rats are smarter than Norway. Sometimes you get a little puzzled by traps being set off without catching anything. If that happens regularly, is is possible that a (smart) ship rat has discovered that they can set off the trap by pushing on the side of the strike plate until it trips. Some loose a leg by doing it, but often it just gives them only a fright, they run off, but are back not long after to collect the spoils of their effort.
One way (not sure if there are other) of dealing with this is putting the inside mesh upside down (MUD). This forces them to climb over the mesh and when they jump down, there is no way back.
It doesn’t appear to be a problem for other predators, maybe apart from older Norway or the not so smart ship rats. I have caught all sorts in that way, incl. a younger possum, rabbits, stoats, weasels and of course lots of rats. Once you caught the smart ones, you can turn it around again, if you like.
MUD will probably prevent Tuis taking their chances, if that is a risk in your area.
Photos of a stoat and a rabbit caught this way. (Ooops As a ‘new’ user only 1 photo allowed.)
Willem