just another note the islamic calander actually is 12 months of between 29 and 31? days giving a total of about 354 days pretty much a lunar year so you can see why it shifts with respect to the seasons due to being less than the solar year. However a 13 month year of 364 days should not shift as much and cause confusion to seasons but would probably end up pretty out of sync with the moon as a lunar month is actually about 29.3 days long. So it would all depend on what was being used to guide these people.
caroline x