The growing electricity demand, combined with the increasing integration of photovoltaic (PV) generation into the distribution system, requires higher flexibility from the demand side. This paper proposes a customized scheduling approach for demand response (DR) of customers with dispatchable inverters in distribution-level PV facilities. Based on the Chilean context, the proposed approach enables these energy resources to provide flexibility in the technical and economic management of the distribution system operator (DSO). Specifically, a bi-level optimization model is introduced. At the upper level, the DSO minimizes distribution system costs by determining daily price signals for customers based on their response profile classes (RPCs) and active and reactive power set points for PV facilities. At the lower level, customers aim to reduce their electricity bills. In addition, the proposed approach ensures the reliable operation of the distribution system with high probability by addressing uncertainty through chance constraints (CCs). Incorporated CCs in the distribution system modeling include the squared magnitude of nodal voltage, complex power flow in lines, and apparent power of inverters. Finally, two case studies are presented, involving 420 residential and commercial Chilean customers with two distribution-level PV facilities using real-world market prices and daily consumption profiles on the IEEE 37-node test feeder. Results demonstrate how the proposed model enables the customized scheduling of customers and PV facilities, highlighting its effectiveness over the uniform price scheme.