I have a map service and a feature service from an AGS that I manage. I added the data to a web map (and also to a BETA web map - Esri's newer version of the AGOL web map) and am experiencing the same issue:
The current time is clearly 12/31/2008 - 12/31/2009, but the slider shows 2009-2010. ???? I don't even know what to make of this. The time settings established in ArcGIS Pro look like this:
This is what was used to make the services. The time displays correctly in ArcGIS Pro.