Unless you cancel an order for the work you purchased, you own all the rights. The Seller cannot share, advertise or promote themselves with material you purchased unless you state otherwise. This is what users agreed to during sign up per Fiverr’s Terms of Service.
From Fiverr’s TOS: "Ownership and limitations: Unless clearly stated otherwise on the sellers Gig page/description, when the work is delivered, and subject to payment, the buyer is granted all intellectual property rights, including but not limited to, copyrights for the work delivered from the seller, and the seller waives any and all moral rights therein. The delivered work shall be considered work-for-hire under the U.S. Copyright Act. In the event the delivered work does not meet the requirements of work-for-hire or when US Copyright Act does not apply, the seller expressly agrees to assign to buyer the copyright in the delivered work. All transfer and assignment of intellectual property to buyer shall be subject to full payment for the Gig and the delivery may not be used if payment is cancelled for any reason. For removal of doubt, in custom created work (such as art work, design work, report generation etc.), the delivered work shall be the exclusive property of buyer, and seller assigns all rights, title and interest in the delivered work."
If you haven’t already, I would strongly recommend you read up on the terms. This way you have a better understanding of Fiverr and the terms you agreed to: http://www.fiverr.com/terms_of_service This will prevent any potential issues or confusion in the future!