I think hydrophobic is the more technical term (instead of aquaphobic), but in this case I'd call what you're witnessing more of a wettability problem.
Two of the multiple material characteristics that can affect wettability are the chemical makeup of a surface and/or the structure of a surface.
By chemical makeup I'm talking about the surface energy of the surface - hydrophilic surfaces tend to have higher surface energies whereas hydrophobic surfaces tend to be lower. As soil is made up of materials such as clays and silicates, you would expect them to wet readily. However, some organic components mixed into the soil or even on the soil particles themselves can reduce surface energy. Fungi, for example, are very good at synthesizing carbohydrate layers that can coat soil particles and render them hydrophobic. In fact, on golf courses they even employ soil-wetting agents (surfactants) to help the water wet the root zones of the grass.
The other characteristic I mention, surface structure, can make high surface energy surfaces unwettable. I believe this is because the high surface tension of water... Google the Lotus Effect for examples.
Anyway, there is a chance that either or possibly both of these factors may be at play. Other factors include the tendency of some components (clays) to swell when wetted, hindering the penetration of water into the "balls" of dirt that are swept up when you dump a bucket of water over it; the fine particle size of dirt you'd find under a mat also likely plays a role. Wetting insoluble powders can be a major challenge in industry, and is usually solved by vigorous mixing (sometimes using high shear) and/or surfactants.... which leaves me somewhat surprised that the surfactants in your mop water did help wet the soil.
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