You can manage data access permissions for your project using the options found in Manage Project at the bottom of the page. This will affect how the public sees your data. Regardless of the permissions you set, each time data from your project are downloaded it is logged in your Data Access Log.
Data Access Log
Accessed from the Manage Data landing page, the data access log includes an entry for each time data from the project was downloaded. This includes a date/time of download and the user who downloaded these data.