Dates are stored in the database as UTC offset (ie GMT+0).
When emails are delayed for an hour this usually suggests to me that people aren't allowing for daylight savings correctly.
If you look at your processes and specifically the (green) automatic actions that send out the reminders, then check the "Send Date" field. Right click and show the calculation.
Is it setting the return value to DateTime.UtcNow or Datetime.Now ?
I suspect the latter and hence why they are an hour out. Always set dates to UTCNow is the usual tip.
Ugh... yes. When I reviewed the Process, I noticed that the Add Reminder actions are formatted inconsistently. In most cases, it is set using DateTime.Now so I will need to change those (need to use proper change management). I also noticed that some of the actions Send Date field is set to December 13, 2007 and others that have the right date:
Notifications seem to be a real concern for us outside of the delay I mentioned above. We are also having an issue whereby when someone adds a Note to a ticket, and enables both the Notify Requestor AND Notify Assignee, that sometimes the Assignee doesn't get the notification. We have also seen where the Requestor does not get the notification on Notes as well...
Setting the dates in the past is the way we used to ensure (as design consultants) that the reminder would be sent immediately at runtime as well before the time we could right-click and set it by a calculation to current date/time.
Normally that date is a good barometer for when those reminders were originally added to the process design.
Also re the "...Notify Requestor AND Notify Assignee, that sometimes the Assignee doesn't get the notification".
If you look at your screenshots it is pretty obvious when those checkboxes are ticked on the form.
Not so obvious is when there is a calculated or value type set against it as then just look blank.
For your 2 feature checkboxes to work you have to be setting the value in the reminder checkboxes based on the checkboxes on the note window; that's how it works.
I'd hazard a guess that they are not setup correctly at some statuses in the process and thus why observed to be working inconsistently.
Finally, don't get confused by the "Notify Assignee" checkbox; it DOES NOT just work if ticked alone. What that label should really say is notify whoever is ALSO filled in in one or more of the GROUP'/ROLE/USER dropdown lists. So if that checkbox IS ticked also look for static values or value types (as per your screenshot) in this 3 fields as well. You'd not be surprised at the many customers I encounter in my travels that are complaining it is not working when they have really just fallen foul of the above rules and simple to fix.
Hope you fix OK.
In addition to what JulianWigman has pointed out, it might be worth checking the process around the add note action. It's possible that while you are ticking Notify Originator or Notify Assignee the process under certain conditions will not be fulfilled because of the conditioning in the process.