"Effectively"? It sounds like a $1 booking fee (operational fee per booking for the service provider) plus a percent of total service provided (i.e. miles). This means you get billed for using the service to get a cab ($1), plus they get a cut of the total transit mileage (10% fare). That seems fair and normal for this sort of business--I mean hell, pizza delivery services charge a fucking delivery fee that doesn't go to the driver as a tip, because they have to idle and coordinate drivers while paying them a wage.
Pizza delivery places don't take the delivery charge out of the tip. That's in addition to the tip. If Uber added the "10% of fare" and "$1 booking fee" directly to the pre-tip amount owed by the passenger, then that would be fair. Making the cab driver pay for the privilidge of having the service target his company is inappropriate.