Deposit before the services are performed is not revenue and should not attract Chinese tax right away. As the service is enjoyed by the user and the deposit is converted into revenue, tax obligation will arise accordingly.
In practice, if the foreign website has affiliates in China, and the payors are all Chinese individuals, there is not an effective mechanism to collect tax at this point. Usually in such situations, even if some Chinese tax obligations may arise on technical ground, the primary way to collect the taxes is through withholding by the payors in China. If the payors are all individuals, it is unrealistic to expect them to withhold the Chinese taxes and settle them with the Chinese tax authorities.