The EU legislates product safety by making the person who made it available within the EU legally responsible. This is always an EU based entity. If you want to sell something which falls under a range of product classifications within the EU, you have to take responsibility for that product's safety.

Yes, manufacturing may happen overseas, but generally the product is still sold to the consumer by a locally based entity. Legislating that sellers are always responsible for disposing of products they sell isn't hard - we already do it for electronics with the weee directive.