Given your setup, the path should start at 8:00 AM, get to the middle stop a short while later and then depart at 9:00 AM and end the path at the third stop around 9:03 AM. So can you double check that the ending time on the third stop is 9:03 and not 8:03 Also, can you bring up the properties of the middle stop and check that the time windows start and end are set to 9:00 AM and 10:00 AM?
Your screen shots for the attribute tables for bb show the TWStart1 and TWEnd1 are on the point feature class. BUT, do you load these values to the Stops when you do Load Locations? That is, open the attribute table for Stops and see if these values are set on the Stops TimeWindowsStart and TimeWindowsEnd columns. If they are not set then you need to reload your stops by maping these fields when you do load locations so that the values load in.
Your attached zip file cannot be downloaded as it says it's corrupt.
If the Stop properties are null, then you need re-load your Stops. But when you do that, on the Load Locations dialog, make sure to map the time window fields and then open the Stops attribute table to see that the values have been set.