As explained in the First configuration part of this guide, the EAN Exemption option works only during Product creation process.
If your account is enabled for EAN exemption and your Prestashop products don’t have that code, in order to sync offers you need to set the Prioritize ASIN code to  Yes in the Sync tab and choose Reference or Supplier reference as SKU in the General tab. Now you can procede with one of the following methods:

• if the product is already present in your Amazon inventory and Prestashop SKU is different from the one on Amazon, you can manually insert the ASIN code in the AmazonSync tab within the product sheet in Prestashop. Because of the different SKU the offer will be duplicated in your inventory: it is necessary to delete the old one or make sure that Amazon’s and Prestashop’s SKUs match;
• if the product is already present in your Amazon inventory and its SKU matches the one in Prestashop, you can download your inventory using the dedicated buttons at the bottom of the Sync tab within the module. Doing this AmazonSync will automatically link the ASIN code to each Amazon SKU found in Prestashop too;
• il the product does not exist on Amazon you will have to follow the Product creation procedure, paying attention to the dedicate EAN Exemption section.