Tokens are debited automatically throughout the show duration.
Note that while the private rate is 'per minute', they are actually debited every 10 seconds - for example, if the private rate is 42/min you will be debited 7 tokens every 10 seconds.
ETA: not to be overly pedantic, but the tokens are debited from when the model accepts the private request, not from when you click the 'start private show' button.
Further ETA (I'm on a roll!): it's likely there will be a minimum private show duration set by the model, so if you end the show early you will still be debited the minimum number of tokens (per min rate x min duration), so always check the model's terms in the pop-up window before you click start, to make sure you understand.