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The Manichaean Calendar was a lunar based (luni-solar) one where months began on the new moon:

"Annual recurrence of holidays. The Sogdian calendar-lists published by W. B. Henning (1939) provide reliable information about the names of the annual celebrations. To them should be added the manuscript fragment 6191 of the Otani collection of Ruykoku University, Kyoto.

The annual celebrations of the Manichean church were determined by the lunar year of the Babylonian calendar  as it had been known by Mani. Holidays were determined by the position of the sun in the ecliptic and certain phases of the moon. Commonly they fell into the latter third of the Babylonian luni-solar year (Sagittarius to Pisces). Calendar lists which had to be created every year anew were used for the conversion of these dates into the common Sogdian calendar (Henning, 1945, pp. 151-52; Taqizadeh, notes to Henning, 1945,pp. 158-59)."- SUNDERMANN

The various scholars and authors who suppose that the Manichaean Calendar was a solar one are in error. It was consistant with the ancient lunar calendar (Shawui) once in use by the Nazoreans.