It doesn't really matter where the data comes from, date fields are handled the same way.
If you are loading this CSV directly into the map, the ArcGIS.com map viewer doesn't have any option to specify the field type of the Date field. It gets imported as a date field, and the browser will adjust the display according to the browser's local time. However, ArcGIS Explorer Online will let you choose a field type as "text" instead of date. So, you can initially upload this CSV layer into the web map using Explorer Online.
Alternatively, you can create a feature service out of your CSV. By adding the CSV as an item to your My Content, you have the option to publish a feature service, and also specify that the date field should be imported as a string field.
Thanks,
Mike