In my NO-BATCH TSI deployments, I see that a job that takes more execution time skips any transition to the Running state. During the execution phase it continuously returns the QUEUED state until the STAGINGOUT/SUCCESSFUL state is reached. It means except Running it doesn't miss other states STARTED / STAGINGIN / STAGINGOUT / SUCCESSFUL.
This behavior is not observed while running the same job on a Embedded or batch-TSI deployments.
As an example I am submitting a "dd" job that generates a big file of size ~5-10 GB. For reference the sample jsdl instance is attached under. Of course data staging target needs to be adjusted to your path. By the way I see the same behavior while submitting long sleep jobs.