Probably internal warfare and the breaking of peaces:

“These clans—located largely in the mountainous regions beyond the wolfswood, in the high valleys and meadows, and along the Bay of Ice and certain rivers of the North—owe their allegiance to the Starks, but their disputes have oft created difficulties for the Lords of Winterfell and the Kings of Winter before them, forcing them to send men into the mountains to quell the bloodshed (commemorated in such songs as “Black Pines” and “Wolves in the Hills”), or to summon the chiefs to Winterfell to argue their cases.” (WOIAF)

I would guess what happened is that the Starks took hostages when they sent men into the mountains to prevent a further outbreak of violence, and then someone was dumb enough to break the peace, and to prevent another war and another intervention from Winterfell, a Stark cut off some heads to show that they would enforce the peace personally if they had to.

So it’s not about disloyalty to the Starks, it’s more about the folkways of feuding and vendetta.