Accordingly to the legend, people responded to the call and managed to drive the Mongols out of China and led to the founding of the Ming Dynasty, 明朝, in 1368.
Historical version
In 1271, the Mongols established the Mongol Dynasty or Yuan Dynasty, 元朝, and by 1279, defeated the Chinese Southern Song Dynasty, 南宋.

The Mongols introduced four social categories for their subjects. The top of the hierarchy were Mongols followed by Western and Central Asians, former subjects of the Jin Dynasty (including Chinese) and the bottom were the former subjects of the Southern Song Dynasty (mainly Chinese subjects).

The results of Mongolian economic policy such as tax farms and inflation as well as land management failures caused much hardship especially for those at the lower end of the hierarchy, the former subjects of the fallen Southern Song Dynasty.

Socially, there controls targeted at the Chinese population. Chinese subjects were not allowed to gather in public, could not own weapons. At one stage, Kublai Khan even forbade Chinese from using bamboos as it could be used to manufacture bows and arrows. There were certainly constrains in communication as well.

The various policies resulted in much resentment against the Mongol rulers and many Chinese scholars refused to serve the Mongol government. In less than one century, the Mongol rule over China weakened and various rebellion movements rose to challenge the dynasty.

By 1355, one of the rebels, Zhu Yuan Zhang, 朱元璋, emerged as the leader of the rebellion movement. In 1356, he captured Nanjing, 南京, and used it as his based to consolidate his power against other rebel groups.  In 1367, Zhu Yuan Zhang sent troops north towards the capital of Yuan Dynasty (today’s Beijing).

On 14 September 1368 (2nd day of the 8th lunar month), Zhu Yuan Zhang’s troops entered the Mongol capital and the Mongol Emperor Toghun Temur retreated into Mongolia.

Zhu Yuan Zhang declared the establishment of the Ming Dynasty, 明朝, and made Nanjing the capital of his new dynasty.

Legend : http://www.chinatownology.com/mooncake_and_mongols.html

Mooncakes have played a central role in Mid autumn Festival traditions. Once, according to Chinese legend, mooncakes helped bring about a revolution.  The time was the Yuan dynasty (AD 1280-1368), established by the invading Mongolians from the north. The Mongolians subjugated the Han Chinese.

According to one Chinese folk tale in moon cakes festival , a Han Chinese rebel leader named Liu Fu Tong devised a scheme to arouse the Han Chinese to rise up against the ruling Mongols to end the oppressive Yuan dynasty.

He sought permission from Mongolian leaders to give gifts to friends as a symbolic gesture to honor the longevity of the Mongolian emperor. These gifts were round mooncakes. Inside, Liu had his followers place pieces of paper with the date the Han Chinese were to strike out in rebellion — on the fifteenth night of the eighth month.

Thus Liu got word to his people, who when they cut open the mooncakes found the revolutionary message and set out to overthrow the Mongols, thus ending the Yuan dynasty.

Today, far from the exotic and heroic legends, Chinese communities all over the world make and consume mooncakes during the traditional autumn Moon Festival. In San Francisco’s Chinatown, during the eighth annual Moon Festival, many stores will be selling modern-day of autumn mooncake, the continuation of an honored tradition.

Source: http://www.moonfestival.org/overview.htm

Since the first day of 8th lunar month is 9-14-2004, the Moon Festival is on 9-28-2004 in China time zone. The Moon cakes Festival is on the same day 9-28-2004 in USA time zones, since the new moon day is on 9-14-2004, too.

Time is the standard time, not the day-light saving time

Year 2004, the autumn mooncake is on the full moon day. The full moon time is at night. If you watch the moon on 9/28/2004 at Chinese Moon Festival night, you should feel the moon is fuller than previous years.

The Moon Festival is a holiday in China. It’s an occasion for family reunion. Chinese families like to get together to eat the moon cakes and watch the moon at the Moon Festival night.

For the people are out of town or for Chinese are from China stay in USA, they miss their family or the lover at home and share the same moon at the night of the Moon Festival before the Internet gets popular.

In China Time Zone, the Chinese Mid-Fall Moon Festival coming days are 9-25-2007, 9-14-2008, 10-3-2009, 9-22-2010, 9-12-2011 and 9-30-2012.

Source: http://www.chinesefortunecalendar.com/midfall2004.htm