Blackcaps not growing new canes

[Purrfluff]

Last year I put in four "Jewel" black raspberry plants. One took off and produced a bunch of canes. These canes are now fruiting and look healthy and happy. However, there are no new canes (primocanes). At all. I would have expected it to start putting out primocanes by now. If it doesn't produce new canes not only will there be no fruit next year there will be no plant. It won't have leaves to photosynthesize with. Also, my understanding is that after fruiting I am supposed to cut the canes that just fruited. If I cut those canes there will be no canes, period.

Am I just not waiting long enough? My trailing blackberries have already started putting out new canes and their fruiting is only a couple of weeks ahead of the black raspberries.

If I don't see any new canes I will just leave the fruiting canes in place the plant has some leaves to keep it going.

The other three plants are much smaller. One does have a single fruiting cane but it has a couple of (rather short) non fruiting canes. Their size and behavior is more typical of a bare root plant.

When the large plant put out all those canes last year it also tip rooted a bunch of plants. I am growing them on in pots but if their parent is some kind of weird mutant I don't know if I should use them.