Then it's probably from an item then. There are a handful of default attack replacers besides cadence, some of them like troll rage and beronath's fury are from items.

Depending on your build, you can choose not to have a default attack replacer but rather use a weapon skill with a cool-down and just rely on a normal default attack being used during the skill recharge period, in which case maybe it wasn't a default attack replacer at all (and the list of attack skills from items is a lot bigger than that of default attack replacers).

Anyway, cadence is still powerful attack that works well despite the minor limitation you mentioned, so it really depends. You can choose to build around cadence or ignore it for something else.

I haven't really played around with cadence much myself, but if I was going to build around cadence it would probably be a dual-wield blademaster build focused on attack speed to get that third cadence hit off as much as possible and minimize the loss of the on-hit procs 1/3 of the time. But someone who has made serious cadence builds may or may not give you different advice.