Hi Guido,
is this perhaps DP 8.1+? The advananced scheduler coming with that release is entirely orthogonal to the existing one, you will not see the schedules where you used to see them, they will not show up correctly in the view of backup specs sorted by next run, and they will not even take notice of omnitrig -stop and run anyway (there's a new maintenance mode for that).
BTW, given you have Exchange specs, they tend to trigger sessions initiated by the client towards the server, for instance if something went wront with some of the stores on the initial run. The ultimate trigger for them is still a properly scheduled backup spec, though, so nothing coming from the Exchange server entirely on its own schedule. Other integrations may work differently (SAP comes to mind), but you don't seem to have such special cases.
HTH,
Andre.