How Hindu Civilization came to Majapahit is not very clear yet. The information above is just some theories that could be right. However we know that Majapahit was an Kingdom that was influenced by many cultures in its development. For example Hindu and Islamic culture.
Majapahit was mostly influenced by India. However Majapahit was not there when the Hindu civilization was spreading to Java. In some stories they say Aji Saka introduced Hindu civilization to Java in 78A.D. He is also known as Agastya and is commonly seen in some Javanese Hindu temples. He can also be called Shiwa as a teacher. Others say that immigration and colonization by Indian merchants brought Hinduism and Buddhism to Java. This theory is an older theory however it could be correct. However the oldest evidence found of Hindu civilization is in Borneo. Some stone inscriptions were found from around 400A.D. Those stone inscriptions mentioned the reign of a King and were written in Sanskrit. Civilizations all over java were influenced by Persia, China, Europe and India from Traders and Religious cultures. The people of Majapahit are very quiet, polite and reserved. Their main ethnicity is Javanese but they did have Indian merchants and Chinese merchants stayed at some of their Ports like Port Bubat.

"BALI AND INDONESIA ON THE NET: Welcome to Java." 9 Oct. 2006

"Memory of Majapahit:Introduction." 9 Oct. 2006