The positions of the two solstices between the stars shift about 50 arcseconds per year (compared to the stars) because of the precession of the equinoxes, and happened to cross the adopted center line of the Milky Way around the beginning of 1999. This happens about once every 13,000 years. In star atlases that use the equinox of J2000.0 the distance between the solstices and the center line of the Milky Way is only about 50 arcseconds or 0.014 degrees, and such a small angle can only be discerned in very large star atlases. There is no physical reason for a connection between the plane of the Milky Way and the plane of the orbit of the Earth, and the precession did not notice that the solstices crossed the center line of the Milky Way.
