Do I comply with the Directive once my company has become a member of a collective take-back system in a given member state for the products or do I have to fulfil other obligations as well?

In the event the compliance scheme is taking over all responsibilities of administration, logistics and recycling from the individual producer or importer of products, the company needs to assess individually and on a case-by-case basis its financial responsibility. You might need to seek further guidance with your accountant for these matters.