I don't think theres an official scheduled time thing aside from the hours they are available for offline privates, that would just be something discussed between model and user, the user can only click the button and then the model has 10 minutes to accept or decline.
Keep in mind that the member is not given any information about the 'hour range' that the model is available for the offline private, only that she is 'available' for offline privates.
The only feedback that the member receives is from the verbiage contained in the request box that states the model has '10 minutes to accept or deny the request, and that the member will not be charged if she declines the request'. Which would lead the member to think that the private would start within those 10 minutes if she accepts the request, but yummybrownfox indicates in her reply above that a time is(or can be) scheduled between the member and the model on when the private will occur.
What communication method is used to discuss the scheduling of this time if the model is offline on the main SC site, where no PM's are even possible?
So now the sequence of events seems to be something like this..
1. A member requests an offline private using the button on her SC page
2. The model receives the request via Plasma
3. The model has 10 minutes to accept or decline the request. How she accepts or denies the request, and how the member is notified is still in question.
4. If the model accepts the request, it would appear that the member is then locked into paying for the show. So what happens if the model accepts the request, but is unable to do the private until several hours later when it is not possible for the member to be there?
Edited to add: The model I referenced in my earlier screenshot has now been offline for 7 days, but it still shows that she is available for 'offline privates'.