Causality breaking is subtle. For a simple one-way trip, in your reference frame, nothing will seem wrong, but from another reference frame you may appear to go back in time. If you have two pairs of ansibles (FTL telephones), each pair moving relative to the other, it's possible to send a message round trip (FTL to your connection, normal space to another endpoint, FTL to its connection, back to you) in such a way that you receive it before you send it.
Sorry, my English is terrible, so I don't quite get it.
An example would be good. Let us say that Alice is communicating with Bob who is on a planet 12 light years away with messages that travel at 4*c speed. All the while Alice is travelling towards it at 3*c.
I am not sure how this "FTL to your connection, normal space to another endpoint, FTL to its connection, back to you" would end up reaching Alice before she sends the message.