I have never had a problem with any of my pans heating up on my induction burner; in fact, when I first started using it, I was amazed at how fast they heated up! I always said that if I ever had to move, and get a non gas range, it would be induction, after using that.
That definitely sounds like some bad product, with simply some bad, or an insufficient amount of the magnetic metal in the base. Thinking about this, I took a magnetic dish - some things I keep screws, nails, and things like that in, in my workshop and outside, which have a magnetic disk in the base - and put it on the bottoms of many of my induction capable pans, then pulled it off. The one pan, which is the only one I noticed that was slightly slower heating up, was definitely easier to pull off, and the carbon steel wok almost yanked it out of my hand, and was the hardest to pull off. All were fairly strongly magnetic, and even the tea kettle with the very thin metal, was strong, which didn't surprise me, as that thing boils the water slightly faster than the gas, unless I have it on so high it's up the sides! And the enameled CI also seemed strong, so that coating doesn't seem to weaken it.
So check the magnetic capability of those pans - maybe it has something to do with that? I would have thought they'd have that standardized by now, but we know how that goes!