Every teacher and every other employee of the school districts for which the plan for district retirement is adopted, who is employed by the districts at the time of the adoption of the plan, and who signs an agreement to be subject to the burdens of the district retirement plan, shall be entitled to the benefits and subject to the burdens of the plan and of this chapter. Every teacher employed in the public schools of the districts after the adoption of the provisions of this chapter by the governing boards of the districts, and any other employees the boards or the petition determines, shall be bound by the benefits and burdens of this chapter.