The paper is devoted to detecting output races in distributed systems. We perform such detection through testing their implementations. As an underlying model for our test generation strategy we consider a Timed Finite State Machine or a TFSM (for short), where each input/output transition is augmented with a timed guard and an output delay. A potential output race can thus be simulated as an output delay mutant; this formalism is introduced in the paper. In order to build a test suite, we adapt a well-known test generation strategy, a transition tour method. The novelty of the proposed method relies on choosing appropriate timestamps for inputs, yielding a timed transition tour. We discuss its fault coverage for output race detection. As an application case study, we consider a Software Defined Networking (SDN) framework where the system under test is represented by the composition of a controller and a switch. Experimental results show that the timed transition tour can detect races in the behavior of the widely used ONOS controller.