Sequential reactive systems are formal models of programs that interact with the environment by receiving inputs and producing corresponding outputs. Such formal models are widely used in software engineering, computational linguistics, telecommunication, etc. In real life, the behavior of a reactive system depends not only on the flow of input data, but also on the time the input data arrive and the delays that occur when generating responses. To capture these aspects, a timed finite state machine (TFSM) is used as a formal model of a real-time sequential reactive system. However, in most of known previous works, this model was considered in simplified semantics: the responses in the output stream, regardless of their timestamps, follow in the same order in which the corresponding inputs are delivered to the machine. This simplification makes the model easier to analyze and manipulate, but it misses many important aspects of real-time computation. In this paper we study a refined semantics of TFSMs and show how to represent it by means of Labelled Transition Systems. This opens up a possibility to apply traditional formal methods for verifying more subtle properties of real-time reactive behavior which were previously ignored.