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This paper investigates the scheduling problem of a fleet of electric vehicles, providing mobility as a service to a set of time-specified customers, where the operator needs to solve the routing and charging problem jointly for each EV. Hereby we consider incentive-aware customers and propose that the operator offers monetary incentives to customers in exchange for time flexibility. In this way, the fleet operator can achieve a routing and charging schedule with lower costs, whilst the customers receive monetary compensation for their flexibility. Specifically, we first propose a bi-level optimization model whereby the fleet operator optimizes the routing and charging schedule accounting for the spatio-temporal varying charging price, jointly with a monetary incentive to reimburse the delivery time flexibility experienced by the customers. Concurrently the customers choose their own time flexibility by minimizing their own cost. Second, we cope with the computational burden coming from this nonlinear bi-level optimization model with an accurate reformulation approach consisting of the KKT optimality conditions, a Big-M-based linearization method, and the zero duality gap of convex optimization problems. This way, we convert the proposed problem into a single-level optimization problem, which can be solved by a strengthened generalized Benders decomposition method holding a faster convergence rate than the generalized Benders decomposition method. To evaluate the effectiveness of the proposed mathematical model, we carry out numerous simulation experiments by using the VRP-REP data of Belgium. The numerical results showcase that the proposed mathematical model can reduce the delivery fees for the customers together with the cost of operation incurred by the fleet operator.