The Muhajireen refused to join the army of Usama because...
The Muhajireen refused to join the army of Usama because they knew the purpose of the Prophet (a.s.) by marching this army. It was to make Medina empty of the companions after the Prophet’s death so that Imam Ali (a.s.) would assume the caliphate easily and without troubles. Therefore, they refused to join Usama whom the Prophet (a.s.) had appointed a leader over an army to march towards Sham.
Umar said to Usama, ‘Do the messenger of Allah die while you are the emir over me?!’ The Muhajireen denied the homage that the Prophet (a.s.) had taken for Imam Ali (a.s.) in Ghadeer Khum to be the caliph after him. They said, ‘Muhammad thought that this matter (the caliphate) had already been fulfilled for his cousin. How far! It shall not be fulfilled.’ [2] [1] The Muhajireen (immigrants) were the first Muslims who had emigrated from Mecca to Medina.
[2] The Life of Imam al-Husayn bin Ali (a.s.), vol.1 p.235. They revealed that in their meetings and so their news reached the Ansar. They also denied that prophethood and the caliphate would gather in one family. When the Prophet (a.s.) died, Umar announced before people, ‘Prophethood and the caliphate should not gather in one house (family).’ They denied the gathering of prophethood and the caliphate in one house which was the center of the revelation, wisdom, and faith.
And it was so as they wanted. The caliphate was extorted from the Ahlul Bayt (a.s.) and turned to be in the hands of the opponents of Islam; the Umayyads and the Abbasids who ruled unlike what Allah willed, and whose palaces were stages for debauchery, drinking, singing, dancing, and all sins, whereas the Ahlul Bayt (a.s.), who were the compare of the Qur'an, were treated cruelly and their heads were raised on the tips of spears, and their women became captives taken from one country to another.
It was this that Quraysh wanted in order to revenge on the Prophet (a.s.) through his progeny. Second, the Ansar were certain that if the Muhajireen seized power, they would subjugate and oppress the Ansar as revenge. Al-Hubab bin al-Munthir, who was one of the chiefs of the Ansar, declared that by saying, ‘…but we fear that those, whom we had killed their sons, fathers, and brothers, may assume it (the caliphate).’ [1] Actually, the prediction of al-Hubab came true.