I've tried to do something similar with a personal account and no ArcGIS server, without much success. I found this tutorial, on the esri site. Not sure if it addresses your problem but hopefully it can help.
Sarah
ArcGIS Online hosted tiled map services don't currently support time enabled layers.
Thanks,
Mike
Hosted feature services don't currently support time. It's something we want to support and will release when available. So, there is no hosted way to support time aware layers. You need to have ArcGIS Server currently to do this.
When you "share as" from ArcMap, you get a tiled map service by default. You need to explicitly enable the feature service capability (and optionally turn off tiles if you don't want them).
Thanks,
Mike
It's only been a few months, but has this capability been added to ArcGIS Online yet? I've been trying to upload a feature service with time series info and haven't been able to figure it out. I'm guessing this still isn't implemented yet, is that correct?