It's a fair question because "each" is a singular and "us" is a plural. In this case, each is the subject of the verb become, so the verb is singular : "... becomes ..."
However, each can be used differently with a sentence having a similar meaning : "We each become ..." here the subject of the verb is we so the verb is plural. The "each" here is like an adverb (?) with the meaning of "all of us one by one" and is not the subject.