ADA Notification Act of 2013 - Amends the Americans with Disabilities Act of 1990 to deny jurisdiction to a state or federal court in a civil action a plaintiff commences for remedies for disability discrimination in public accommodations and certain services provided by private entities unless: (1) the plaintiff notified the defendant in writing of the alleged violations prior to filing the complaint, (2) the notice identified the specific facts that constitute the alleged violation, (3) a remedial period of 90 days elapses after the notice, (4) the notice informed the defendant that the civil action could not be commenced for 90 days, and (5) the complaint states that the defendant has not corrected the alleged violation.