Outer flow and boundary flow are often different.
Do tufts at the wing surface show boundary layer flow or outer flow?
Paint shows boundary layer flow.
The boundary layer being the layer of flow with less velocity than the free stream, and which can be from nearly zero at a leading edge to an inch or two thick at a trailing edge, you can say that tufts are generally showing boundary layer flow except on or near leading edges where the flow is laminar and the boundary layer is so thin, the thickness of the tuft may put part of it in the free stream.
But as soon as the laminar part of the boundary layer ends and the boundary layer is thicker than the tuft itself, the tuft is pretty much immersed in the turbulent boundary layer. As you go farther aft where the turbulent boundary layer gets thicker and thicker, the tufts may lift off the surface a little bit, hinting at the increased thickness of the BL but not indicating how thick it actually is.
Comments after @JohnK's answer prompt an observation: it depends on the Angle of Attack.
The whole point of having "tufts" in research is to explore areas in the flight envelope where we don't have these nice neat definitions of airflow properties.
Airflow by any name creates lower pressure over the top of the wing by constantly "wicking" air away from the surface (Coanda effect). This "vacuum pump" only works if air is taken away at an equal or faster rate than it can leak back in.
So we have a flow velocity gradient and a pressure gradient as one moves away from the wing surface which maintains the lifting force.
As John mentioned, the boundary layer thickens and becomes more turbulent towards the rear of the wing. Tufts can show this by "wiggling" a bit, but by maintaining their rearward orientation, they are showing the velocity gradient is still intact.
At stall, the pressure gradient breaks down and wing surface airflow becomes chaotic and/or reversed. What better way to show this than with a tuft flopping all over the place.