The actual points transfer is generally instantaneous. How long it takes you to reach an agreement with the owner of the points and transfer money to them is dependent on the people involved.
I just rented some points where I emailed the points owner late on Wednesday afternoon, he emailed back and then I sent him my account info for the transfer and asked him how he wanted me to send him the money. First thing the next morning he transferred the points to me and emailed me the payment instructions, and I sent him the money by Zelle. The points were in my MVC account immediately. So that’s just an example.