The fare that is put on the app by Uber, in terms of legislation, is called the consideration for the supply. It's the price. The tax always applies, in addition to the consideration for the supply. So if only the consideration has been collected from the passenger, the driver will have to collect the tax.
In practice, I suspect it is highly improbable that the app operator will collect, because they will not want an exchange of money between the driver and passenger and because some clients may not do business with them if they cannot have the simplified payment mode.
However, this is a decision for the app operator to make.