I did quickly try this using a point and polygon layer, extracting to a CSV, and then publishing the CSV as a hosted feature layer to check the extraction. Everything worked as expected.
Were it me, I would make sure that you've got your polygon layer set as your Extent layer. If you've inadvertently used your point layer as the extent layer, it's the full extent of the point (or line) layer that is used to set the extraction extent.
If you've done that, then I would scrutinize the polygon layer to make sure there's nothing unusual or amiss.
Another alternative workflow to the Extract Data tool would be to use Find by Attributes and Location, then use Export Data in the Overview tab of the resulting hosted feature layer to export to the desired format.