How does Act I follow the requirement of a Shakespearean exposition?
"Fit," you mean?
Act I presents the background information: Desdemona has eloped with Othello. Roderigo is in love with Desdemona and has hired Iago to win her for him. Iago is plotting revenge against Othello. Brabantio is worried that he will lose his daughter to Othello. The Duke, worried about the Turks, is planning to send his fleet to Cyprus.
Act I establishes Iago as the prime mover. The villain dominates this play. Iago is Janus, the two-faced god of doors: he opens and closes almost every scene. He has more lines than Othello, and he will speak his evil intentions openly to Roderigo and us, the audience, through soliloquy. So, Act I establishes the dramatic irony: we know Iago is evil, but no one else (except for the dim-witted Roderigo) does.
Act I also establishes the setting. Venice, city of reason, stands in sharp contrast to the wild island of Cyprus. Venice, the city of carnival, is where people where masks: Iago pretends to be Roderigo and Othello's friend. Desdemona pretends to be a dutiful daughter. Brabantio pretends to be an upstanding senator. Othello pretends to be a civilized European.
Act I sets the conflict of the play: Iago vs. Othello. Othello wins in Act I, in Venice. He has the Duke to play judge. He publicly defeats Brabantio (and Iago). Othello's voice rings eloquently in Act I. All this will change once on Cypurs. Igao will have more room to plot and maneuver on the island. He will play upon everyone's vices, especially Othello's. Othello's jealousy will rage, and he will lose his power of language and his woman.
Act I shows Desdemona as a rebellious daughter. She will change in Acts II-V to become the paragon of virtue. It's hard to believe it's the same character.