In this paper, the substitutability of the indifferentiability framework with non-sequential scheduling is examined by reformulating the framework through applying the Task-PIOA framework, which provides non-sequential activation with oblivious task sequences. First, the indifferentiability framework with non-sequential scheduling is shown to be able to retain the substitutability. Thus, the substitutability can be applied in another situation that processes of the systems may behave non-sequentially. Next, this framework is shown to be closely related to reducibility of systems. Reducibility is useful to discuss about the construction of a system from a weaker system. Finally, two modelings with respectively sequential scheduling and non-sequential scheduling are shown to be mutually independent. We find examples of systems which are indifferentiable under one model but differentiable under the other. Thus, the importance of scheduling in the indifferentiability framework is clarified.