Hello Michelle, and welcome to the forums!
The water in the cup with the milk resembles the atmosphere because they both are made up of different substances... they both have particles aside from the base of the mixture; they may have different particles (the atmosphere is made up of different substances than milk is made up of), but neither is essentially the "purest" it can be.
The water in the cup with the milk is obviously not just plain water, but has milk particles in it. Similarly, the atmosphere is made up of many gas particles, such as those of nitrogen, oxygen, carbon dioxide, etc. They both carry out electromagnetic scattering, which creates the blue coloring of the sky and the bluish tint of the milk, as the article you linked suggests (if you do not understand any specific parts of the article, feel free to ask and I can explain them more in depth!).
And this leads to your second question: the milk particles and the particles of our atmosphere are not the same, but they both scatter the same colors. Milk contains tiny molecules of protein and fat which scatter blue light, and the sky contains tiny particles which scatter violet and blue light (but our eyes are more sensitive to the blue light so pick it up more strongly). However, it is the size and chemical nature of the particles which determine the wavelength of light to be deflected (so, milk particles and those found in our atmosphere must be similar in these aspects!)
If you do not understand anything above, have other questions, or need some clarification, go ahead and ask.
All the best,
Nithi