Agents have a deal directly with the players, so it depends on the player-agent contract. MLB is not allowed to pay agents directly.
Generally the player will pay his agent after he receives salary. Sometimes this is an annual lump sum and sometimes it is a few installments per year, depending on the player-agent contract.
Acuna could fire his agent today and hire Jay Z but the agent who negotiated the $100M contract likely still gets his cut going forward as Acuna is paid, based on the terms of the player-agent contract.