BTX received in my old BTC address (as seen in the BTX block explorer) , then imported in the bitcore client following the tutorial and it works like a charm.

However, please everybody be aware that by doing just this (importing the private key), the "airdrop" coming from the snapshot won't be considered for the 3% weekly airdrop, as the new income formally is in a different address from the one you have registered for the weekly airdrop.