The important thing is that the high albedo material has to convert incoming light into a particular wavelength of infrared light that is not absorbed by the atmosphere and so it flies straight out into space. If it's just white (high albedo) but doesn't convert light into the right wavelengths of infrared light, then yes, it will warm the surrounding areas because a lot of the light it's reflecting will get reflected off the atmosphere back down somewhere else.
Things appear white because they are reflecting a lot of light in the visible wavelengths you can see, to which the atmosphere is unsurprisingly transparent. Things that are black on the other hand absorb the light, heat up and re-emit at their thermal temperature which in the terrestrial range of 0-100 degrees peaks in the far infrared which the atmosphere is not (as) transparent to.
The linked study is talking about a boundary effect between the cooler area of high albedo (because painting things white does reduce the energy absorbed and reflects a good chunk of that back into space) and the warmer area of normal albedo. Its modelling how that change between different temperature areas affects air circulation and cloud cover, not that the reflected light is warming up other areas.
You are within sight of a blue LED. Does that monochromatic blue look like the blue of the sky? No. Because Rayleigh scattering diffuses higher wavelengths more, not exclusively.
Even a deep red sunset scatters enough light to overwhelm the stars.
Cooling paint emits light deep enough in the infrared that this effect becomes negligible. It proportional to frequency, to the fourth power.
Like a prism, it affects all wavelengths. If it was "specifically that wavelength," "not the rest of it," it would be monochromatic. Like an LED. But it's not. Rayleigh scattering diffuses any near-visible photons, at a rate proportional to their frequency, squared, squared.
That's why cooling paint works differently than merely reflecting light. Even red light can scatter in the air and warm up the environment. Red scatters less than blue... but infrared scatters less than anything visible.