The Tarascans did not outnumber the Spanish because, as in all of the successful Spanish conquests in the New World, the Spanish had lots of indigenous soldiers fighting alongside them. Cristobal de Olíd is credited with conquering the Tarascans in 1522, and he brought with him a mostly Aztec army numbering in the tens of thousands. (We don’t know exactly). But, as you pointed out, the Tarascans let them simply walk across the border and then surrendered to them without fighting.
This happened because in 1521 there was a smallpox outbreak in the Tarascan region (the same outbreak that hit the Aztecs). It killed the Tarascan monarch Zuangua and most of his male relatives. The newly enthroned monarch Tangaxoan II, was very young and inexperienced. His general, a man named Timas, convinced him that the rest of his blood relatives were plotting to kill him and overthrow him. In response, Tangaxoan II had all of the other surviving members of the royal dynasty killed. With all of the royal family eliminated, Timas made a grab for the throne and took Tangaxoan II prisoner. He placed him under house arrest, and tried to talk him into committing suicide. Tangaxoan, however, managed to sneak out through a secret door in the palace and fled to the western side of the lake.
While all of this was happening, the Aztecs sent frantic messages to the Tarascans asking for assistance, but they were all denied. Immediately following the conquest, a Tarascan ambassador was sent to Tenochtitlan where Cortés took him on a tour of the ruins. Cristobal de Olíd then raised an army to go invade the Tarascan region. He arrived at the border in 1522. Scouts on the border informed the border forts, and the border forts sent messengers to the capital, but they got no response. This was about the time Tangaxoan II was sneaking out of the palace to escape Timas, and so the royal court had more immediate concerns. Unsure of what to do, the border forts didn’t do anything. They simply let Olid and his Aztec/Spanish army walk across the border.
At the last second, Tangaxoan II managed to scrounge an army together. He met Olíd outside the lake basin, but then decided to surrender without a fight. Olíd’s army was probably comparable to the Tarascan one, but the Tarasancs were not in a strong position following the attempted coup d’etat by Timas. They also saw what happened to the Aztecs, and decided that they could probably get better terms if they surrendered willingly. And in a sense they did. Tangaxoan II remained on the throne until 1530, and ruled his kingdom as a de-facto independent country within the Spanish Empire. Eventually he was deposed and executed by Nuño de Guzman.
- Cited Source: J. Benedict Warren: The Conquest of Michoacán: The Spanish Domination of the Tarascan Kingdom in Western Mexico, 1521–1530