In the upcoming sixth-generation (6G) era, the demand for constructing a wide-area time-sensitive Internet of Things (IoT) keeps increasing. As conventional cellular technologies are hard to be directly used for wide-area time-sensitive IoT, it is beneficial to use non-terrestrial infrastructures including satellites and unmanned aerial vehicles (UAVs), where a non-terrestrial network (NTN) can be built under the cell-free architecture. Driven by the time-sensitive requirements and uneven distribution of IoT devices, the NTN is required to be empowered by mobile edge computing (MEC) while providing oasis-oriented on-demand coverage for the devices. Nevertheless, communication and MEC systems are coupled with each other under the influence of complex propagation environment in the MEC-empowered NTN, which makes it hard to orchestrate the resources. In this paper, we propose a process-oriented framework to design the communication and MEC systems in a time-division manner. Under this framework, the large-scale channel state information (CSI) is used to characterize the complex propagation environment with an affordable cost, where a non-convex latency minimization problem is formulated. After that, the approximated problem is given and it can be decomposed into subproblems. These subproblems are further solved in an iterative way. Simulation results demonstrate the superiority of the proposed process-oriented scheme over other algorithms. These results also indicate that the payload deployments of UAVs should be appropriately predesigned to improve the efficiency of resource use. Furthermore, the results imply that it is advantageous to integrate NTN with MEC for wide-area time-sensitive IoT.