With superluminal communications in the tachyon antitelephone scenario implies that FTL communications only happen if and only if they don't happen.
However, there are several scenarios where FTL communications can occur and how they work out will be different.
Assume there is a chronology protection principle (CPP), then superluminal messages shouldn't be able to be received in the past. This will remove any problems with causality violation from the picture. This scenario only allows forward in time superluminal communications.
Starting with equation for a round-trip time delay for FTL communications
$T = (\frac{1}{a}+\frac{1-av}{a-v})L$
There are two possible scenarios that are workable.
If the message velocity a is infinite, then the time delay will be almost effectively zero. Any communications delay will be due to response in the FTL communications itself.
If instead of the spacecraft you are trying to communicate moving a t relativistic velocity, it decelerates and comes to relative rest with respect to the position where the transmitter is located. The relative velocity v is now zero. The time delay equation is now: --
$T = (\frac{2}{a})L$
The time delay is due to the superluminal message travelling back and forth between your location and spacecraft you are contacting.
Communications in this scenario requires both parties to be at relative with respect to each other. This can only be done if both you and the ship have agreed in advance when you will communicate with each other. There is almost no point in either party simply deciding to call without prior arrangement. (1)
The usual solution used to resolve causality violation problems is the preferred frame of reference. Vide @JDlugosz's answer for this model. However, there is another resolution, but isn't used commonly, because it isn't easy to wrap our heads around. Essentially superluminal messages travelling backwards in time when they are received they do not come from our future. Instead they come from the future of another worldline (effectively parallel timelines) and this thereby circumvents any causality problems. Causality sequences of events can't be violated, but they can be initiated. This is exactly like the branching timelines model of time travel that also avoids causality violation.
Anyone receiving a reply to their initial message will receive that reply before they send their message, but that reply will come from another future. In fact, because the number of worldlines will be large. There won't simply be one reply, there will be a veritable torrent of them. The problem for the receiver is working out which message is the most useful. Their best approach would be to do a statistical analysis of all messages to work out what is the most probable set of circumstances that is the subject of the message.
If there is only one worldline, then the CPP will manifest itself as the Novikov self-consistency principleNovikov self-consistency principle. The universe will be deterministic. Even if you know the future you will still send the same message, anyway, the reply will come back, into your past, unchanged. Basically there are an infinite number of pathways to achieve the same set of events (always). Also, this model turns the interpretation of backwards in time processes on their head. This isn't causality violation it is now retrocausality.
We are accustomed to causality be about event A causes an event B to happen in its future. With retrocausality event D causes an event E to happen in its past. This starts getting quite confusing when both causal processes are working together in the universe. This usually is resolved as a form of determinism. Again this is Novikov self-consistency.
Finally there is the Antippa Corridor solution where superluminal travel and communications can only go in one direction. If you send a superluminal message to a ship they can't reply with a superluminal message. Any reply can only be send at lightspeed or slower than lightspeed velocities. In which case, you won't need to worry about causality violation of any kind.
The Antippa model would allow one way superlumninal messaging. The geometric shape where FTL messages can be send will be in the half-circle (actually it's a half-sphere in three dimensions) in the direction where tachyons can travel. The ship can only receive messages but cannot reply. You can only send messages to ships within ninety degrees of the tachyon unidirection. There will be an increasing difficulty in sending messages as the width of the angle of sending superluminal approaches ninety degrees.
(1) Almost no point, there might be communications systems set up so if the ship decelerated to relative rest with FTL communications station that could be always listening for messages. You could always accelerate in a vehicle to match the relativistic velocity of the ship you are trying to contact.