If you are using random dithering (the default), the dithering process will not "push" the primary guide star out of the field of view, it specifically avoids doing that. In addition, there is a built-in minimum separation from the edge of the frame based on the user-specified search region, and some session manager apps like Nina will let you specify a central region of interest for auto-star selection - although I would say that probably creates as many problems as it tries to solve. Trying to micro-manage the auto-find process really isn't necessary.
Bruce