I think I can shed a bit more light.
We know from previous discussions on thief that group character modifications are actually implemented by a modification to each individual character. So it is not a big leap to suppose that the karaoke king white song is actually implemented by a modification on each enemy character.
I can also confirm that the white song is a disable, adding a longer disable rune extends the time as expected.
So when you fire the white skill you get:
1. A disable modification applied to each enemy character
2. Karaoke King starts doing a dance animation
The key/bug is to recognise that these two elements start at the same time but are then independent.
So the disable modification wears off each hero based on the tenacity of that hero. You can see this in expedition, King works as expected on low level lines and gets progressively less useful as the lines level up.
The animation wears off after the full time has passed. This means that enemy high tenacity heros will be attacking during the animation. King also can't reapply the disable until the song is finished, leaving a messy window of vulnerability.
The ultimate confirmation of this, if it could be arranged, would be to apply a Karaoke King disable to a group of enemies and see them attack with their white in order of their tenacity.