In the mid-14th century, the Yuan dynasty (the Mongol empire) was beginning to crumble because of the Red Turban Rebellion all over the Chinese mainland. Most of the rebels were former Han Chinese farmers of low birth. Later on, the leader of the Red Turban army founded Ming Dynasty of China and ascended the throne in 1368.
For more information, take a look at the wikipedia.
https://en.wikipedia.org/wiki/Red_Turban_Rebellion
The Red Turban army invaded Goryeo twice.
https://en.wikipedia.org/wiki/Red_Turban_invasions_of_Goryeo
First Red Turban invasion (1359~1360)
In December 1359, part of the Red Turban army moved their base to the Liaodong Peninsula. However, they were experiencing a shortage of war materials and lost their withdrawal route to Chinese mainland. The Red Turban army led by Mao Ju-jing invaded Goryeo and took the city of Seogyung (Pyongyang). In January 1360, the Goryeo army led by Ahn Woo and Yi Bang-Shil retook Seogyung (Pyongyang) and the northern region which had been captured by the enemy. Of the Red Turban army that had crossed the Yalu River, only 300 troops returned to Liaoning after the war.
Second Red Turban invasion (1361)
In November 1360, the Red Turban troops invaded again Goryeo’s northwest border with 200,000 troops and they occupied Gaegyung, the capital of Goryeo, for a short period, King Gongmin escaped to Andong. However, Generals Choi Young, Yi Seong-Gye (later King Taejo of Joseon), Jung Se-Woon and Yi Bang-Shil repulsed the Red Turban army. Sha Liu and Guan Xiansheng, who were Red Turban generals, were killed in the battles. The Goryeo army continually chased their enemy and cleared them from the Korean Peninsula.
What Jung Do-jeon said in ep. 10 is the second Red Turban invasion in 1361.
When King Gongmin of Goryeo decided to escape from the capital, all the Gaegyung citizens were terrified and cried out to think that they were abandoned. Five days after the king left the capital, the Red Turban army occupied the city and set fire to the street. They killed thousands of people and ate the roasted flesh. It’s no joke. Even they went as far as to eat the roasted breast of pregnant women, according to the historical records. (* You can understand why the kids were hiding in the cave in Ep. 10)
King Gongmin of Goryeo prepared to counterattack. He appointed Jung Se-Woon (정세운, 鄭世雲) as the supreme commander. Under his command, Goryeo armies led by Ahn Woo (안우, 安祐), Kim Deuk-Bae (김득배, 金得培), and Yi Bang-Shil (이방실, 李芳實) defeated the Red Turbans one by one, and finally surrounded Gaegyung city. After fierce battles, the city turned into a sea of blood and almost half of the Red Turbans were killed. The remnants fled away to the North.
However, the horrible tragedy began shortly thereafter. In January 1362, three days after they recaptured the capital, the three generals had to murder the supreme commander Jung Se-Woon in obedience to a royal command. In fact, the king’s command was forged by traitor Kim Yong (김용, 金鏞) who was afraid that the war heroes would threaten his power in the court.
Surprised at the news, without knowing the truth, King Gongmin ordered the three generals to come to his temporary palace in Andong, saying he would forgive them all. On February 29, Ahn Woo was the first one to arrive there, and he was killed by Kim Yong’s plot. Yi Bang-Shil and Kim Deuk-Bae were arrested on the way and executed for killing the supreme commander.
In March 1363, one year after the horrible tragedy, traitor Kim Yong sent about 50 assassins to kill King Gongmin staying in Heungwagsa (흥왕사, 興王寺) temple which was used as the temporary palace in Gaegyung.
Eunuch Ahn Do-Chi (안도치, 安都赤) evacuated the king and pretended to sleep in the king’s bed. The assassins mistook him for the king and stabbed him all over with the daggers, but they found out he was not the king. After that, Princess Noguk (노국대장공주, 魯國大長公主) got into the assassins’ way to protect her beloved husband (King Gongmin). The assassins were flustered and hesitated because she was the princess of the Mongol empire, and it could be a serious problem if they killed her. In the meantime, GeneralChoi Young (최영, 崔瑩)‘s soldiers broke into the palace and suppressed the assassins. This 1363 incident is called “the rebellion of Heungwangsa temple (흥왕사의 변, 興王寺─變)”
About 90 people were arrested. Traitor Kim Yong played the innocent and killed all the arrested assassins one by one to hide the truth. However, about 20 days after the incident, it aroused suspicion and he was turned out to be pulling the strings from behind. He continuned to make up a story to clear himself from the charge, but ended up being executed.
* Fact Check
1. What Jung Do-Jeon said about Kim Yong is historically true. But General Kim Deuk-Bae was not his teacher. (There is no historical record about it) Actually, Kim Deuk-Bae was Poeun Jung Mong-Joo’s teacher. Jung Mong-Joo’s funeral oration for him still exists.
2. The kids dying in the cave is a fictional story. The horrible scene is a kind of metaphor for the guilty feeling of present-day South Koreans about the kids dying in the Sewol Ferry disaster in 2014. They died because they obeyed grown-ups who ordered them to stay in the sinking ship and escaped by themselves.
What Boon-Yi said is right. The grown-up means to take responsibility, and there are too many irresponsible grown-ups here in South Korea, including politicians. (sigh)