My Manager
When using a first person pronoun, this indicates the person who is summoned when the customer demands to be proven wrong beyond a doubt, allowing no further recourse, and necessitating the customer’s immediate departure.

The Manager
When referenced using the specific article, this indicates a nonspecific person in charge of saying we’re sorry, with special focus on not making any promises, and a keen ability to lie about apprising the head of advertising about the typographical error.

A Manager
This mythical yet common creature is requested by a customer who believes, before even speaking with you, that you have neither the inclination nor the ability to assist them with their bullshit unprecedented fringe case requirements. 

Your Manager
When indicated using the second person, this references a person who will be annoyed in the future, with whom you will be able to observe and discuss their annoyance.