Hi Tim, sorry for the long delay, I am only seeing this question now.
This is going to be a bit of a long answer, but hopefully it will clear up what is happening. To understand this behavior, you need to understand a bit about what a geostatistical layer is. Don't think of it like a feature or raster layer; think of it like a function. It is entirely in-memory and performs on-the-fly calculations at given coordinates. The layer contains references to the input points and the interpolation parameters, and whenever it needs to calculate a value at a location, it calls a function that calculates the value (for example, the Identify tool actually calls the function at the location you click and displays the result of the calculation in the pop-up). In this sense, the geostatistical layer does not even know its own values except at locations where it has already calculated them, which are stored as cache files. The actual contours that you see are generated by contouring a coarse triangular grid behind the scenes, and the contour lines will have lots of imprecision due to the coarseness of the grid. This will often result in predicted values that are on the wrong side of the contour lines, as you're seeing.
Everything about geostatistical layers is optimized for performance and model investigation rather than cartographic correctness. The layers draw very quickly, and the on-the-fly calculations are what allows the layer to, for example, display cross validation results automatically (since the geostatistical layer contains all the references that are needed to perform cross validation).
The contours are only meant to provide a preview of what the surface actually looks like, and they are not intended to be perfectly cartographically correct. When exporting the geostatistical layer to a raster, the function is called at the center of every raster cell and persisted to a raster dataset, so that is the recommended way to display the final result. Using the Contour tool on the exported raster will provide the most analytically correct contour lines, and it is what I would do if I were in your situation.
In the Appearance tab of the geostatistical layer (in the Ribbon above), there is an option for "Presentation." This will use a finer grid for the contours. This will not resolve all problems with values on the wrong sides of the contour lines, but it will reduce them. The presentation option also appears in the GA Layer To Contour tool.
