Do you have a picture of the pamphlet?
Or just tell the title, and I can look for it online?
Commercial egg producers certainly do adjust the lighting as the pullets grow, to cause egg laying to start at a specific time. Purina's pamphlet may be based on commercial egg production, which uses only certain breeds, and which does not always transfer correctly to backyard chickens.
A pullet might lay her first egg anywhere from 16-18 weeks (about 4 months) up to 8+ months old. It depends on the breed of chicken, the season of the year, the hours of light each day, and a bunch of other factors.