There may well have been other Alderete's who came to Mexico hundreds of years ago.However, the only one that I know of is Julian Alderete who arrived in 1525.
Other Alderete's who came to America include the following:
Jeronimo Alderete who arrived in America in 1535, helped conquer Chile in 1540 and was one of the founders of Santiago.In 1555, he became Governor and Captain General of the Kingdom of Chile.
Gabriel Alderete who arrive in Havanna, Cuba, in 1758. He was the Captain of a frigate.
Ines Alderete who married Juan Barros in Spain 1525.In 1557, they moved to Chile.
The chances that the Alderete's of Mexico are related to the Alderete's of Chile and Cuba are extremely remote.You would have to go back more than 500 years to find a common ancestor.If I were you, I would not spend a whole lot of time learning about these other Alderete's because they will not aid you in discovering your own ancestry.