Even after changing the extent of the GPI layer, Map Tips still works for me. Are you using ArcGIS 10?
The default extent of any geostatistical layer is the rectangular extent of the input points. However, you should think of a geostatistical layer as a function, rather than a final result. It doesn't "know" its own values like a raster does. To find the value at some (x,y) location, the layer has to calculate the result, whereas a raster has a saved value for each cell. The geostatistical layer draws rough contour lines by making the fewest predictions it can to draw roughly accurate contours (this is why the surface often looks different after exporting to raster... this conversion simply entails making a prediction at the center of each raster cell).
Since the geostatistical layer is essentially a function that takes an (x,y) location and returns a predicted value, you can change the range of the (x,y) locations that it will accept. ie, you can change the visible extent of the layer. Changing the range of the x and y coordinates won't change the predicted value at any locations, so that is why the contour lines do not change when you change the extent.
Also, since the geostatistical layer does not have to store all of its values (instead, it stores a function of x,y), it essentially has infinite resolution (up to the precision of your computer); you can keep zooming in, and you will never see pixels like you will with rasters.