"Bill" is the antecedent
"His" is the pronoun that stands for Bill
you cannot go back and forth between 1st person and 2nd person, 2nd person and 3rd person, etc.
Most academic writing is in 3rd person. Do not use the word "I" or "you" in academic writing. Instead, use "they, he, she".
If you are writing about females/girls, you must use female/girl pronouns such as "she, her, hers".
If you are writing about males/boys, you must use male/boy pronouns such as "he, him, his".
If you are writing about both or an unspecified gender, use gender-natural pronouns such as "it, its, they, their, them".
If you use singular pronouns you must use singular antecedents.
"Bill" is the singular antecedent
"His" is the singular pronoun
If you use plural pronouns you must use plural antecedents.
"They" is the plural antecedent
"Their" is the plural pronoun
When you have a compound (2 part) antecedent joined by "and", you will always use a plural pronoun.
"Maria and Denise" is the plural antecedent
"Their" is the plural pronoun
When you have a compound antecedent joined by "nor" or "or" the pronoun agrees with the antecedent closes to it.
The antecedent closest to the pronoun is "musicians".
Musicians in plural. Therefore a plural pronoun "their" is used.
The antecedent closest to the pronoun is "conductor".
Conductor is singular. Therefore a singular pronoun "his" is used.