Can you please explain why Nausicaa is the one who helped Odysseus beat the Phaeacians in the tournament instead of Alcinous? I originally thought it was Alcinous.

They both "help," but in different ways. Nausicaa helps Odysseus after he is washed up on the shore, and Alcinous cares for him after that--due largely to his daughter's initial favor. Since Nausicaa is "first" to help, you could say that she was Odysseus' primary helper.