Silvertate,
Unfortunately the only case in which the social security thing is straightforward is when you are directly employed by an airline with a home base nominated.
There is indeed a transitional period and the new EU legislation allows for aircrew having a flexible base. Whether you are deemed self-employed for tax and social security purposes depends on national legislation in the country or countries involved. There is little straightforward about these cases and one would be wise to consult an expert on the subject and not believe everything your agency tells you.