(Standard disclaimer: Note that everything below is according to my understanding of the issue. I am not a cryptography expert, and am basing these suggestions on the description I've read so far about this bug. Feel free to correct if I am wrong!)
Please note that PFS would only protect past session data which was not otherwise compromised.
However, if due to the heartbleed bug the server's private key was leaked a motivated attacker could abuse this by performing a man-in-the-middle attack on future sessions.
Since, according to the linked article, the heartbeat request can be performed in the handshake phase of the protocol, it is my understanding that an attacker would not even have to be a client of AirVPN.
It would also be technically feasible for client's private keys to have leaked if an attack was performed.
In this scenario, I think the first priority would be to have AirVPN validate their current setup to see if the required upgrades have been performed on all servers. Furthermore, a new private key should be generated for the server (preferrably, if individual Certificate Authorities are used, a new CA should be also generated to sign the server certificate/key, and the new CA certificate should be distributed. This would break current clients from connecting, however, it would give an indication if an attacker is still trying to perform a MITM attack with old stolen key material. Maybe this can be skipped, however, if there is a good way to configure the client to no longer accept the server's old certificate), so future communications are protected.
Furthermore, AirVPN should offer users the ability to generate a new private key for connecting to the service (by downloading a new configuration, etc.).