The agreement between the state and the federal agency shall include each coverage group or retirement system coverage group as to which formal request for the inclusion is made by the legislative or governing body of the employing public agency pursuant to this chapter, prior to the effective date of the agreement. For the purposes of this section, the state shall not be deemed to be a public agency, but nevertheless any formal request for the inclusion made by the Teachers’ Retirement Board upon authorization by the Legislature or by the Regents of the University of California, or by the Adjutant General, shall be deemed to be made by the governing body of an employing public agency.