Spices are absorbed or adsorbed in food?
The answer varies with the type of food and the type of condiment. Both are very complicated mixtures, so a same combination of food and condiment can display varying levels of adsorption/absorption depending on the region/compound being analyzed, but in general, I expect that while all of chemical/physical adsorption and chemical/physical absorption happen to some extent (cooking is quite a messy collection of physical and chemical interactions!), either physical absorption is the most prevalent, or none of them happens to the largest part of the spices.

First of all, adsorption is a surface phenomenon, which fundamentally limits how much matter can be considered adsorbed onto an object. Adsorbed films are usually very thin (probably not much more than a few nanometers thick, often a single molecule thick). Regular macroscopic objects have very little surface area relative to their volume, so it takes a comparatively tiny amount of substance to completely cover the object in a thin adsorbed layer, compared to say, activated charcoal. Thus we can likely exclude adsorption as the main factor.

It's also important to consider that most food is cooked with some amount of solvent (water or oil/fat), and in fact solvents come out of the food while it's being cooked. This means that a lot of the spices can very well end up as part of a liquid (albeit often quite concentrated) solution, which remains stuck on the surface simply due to its high viscosity and significant friction with the uneven surface of the food. I bet this is what goes on in most cases.