A digital elevation model is not representing an optical property of the earth's surface, such as its reflectivity at certain wavelengths, nor is it influenced by the phenomena of refraction or diffusion that occur in the atmosphere.
Instead, it represents the elevation of the topographic surface with respect to a reference surface.
Although the model can be considered to represent these elevations at a given time, it is generally not a kind of instantaneous shot but rather the result of several measurements, even by different methods, at different dates and at different times.
Therefore, as reported by the site that provides the information, the information provided may be considered valid during the course of the year 2000.
Now, it is usual, that for illustrative purposes, we represent the shadows that this elevation model would produce on the surface at a particular time. We call the result of that representation: "hillshade".
If what you need is the apparent position of the sun in the celestial sphere, for a day, at a time and for a particular earth position, there are ways to find out. If you only want to make a shading for illustrative purposes, you could experience the parameters that make your representation produce the meaning you are looking to communicate.