What you want to achieve is a situation where there are tachyon precursors to some kind of what is up until now an unspecified disaster or catastrophe.
Taking a cue from this article about tachyons it is both safe and plausible to assume the tachyon precursor is a non-local event. For example, this might mean that a tachyon precursor happens and is detected all over the galaxy. Now, in this case, everybody, human or alien, with a tachyon detector will know something bad is going to happen -- somewhere in the galaxy.
Perhaps they even know when it is going to happen, but nobody knows where it will be. It is also possible they don't even know when the bad thing will happen. This is fiction and as an author you are allowed some poetic licence. They might even know the magnitude of the disaster.
"That tachyon precursor they detected last week, that was big enough to destroy a planet."
"As long as it's not our planet I don't care," he replied.
"But it could be," she said gravely.
This suggests there are three variables you can play around with depending whether the tachyon detector has enough information to know about (1) when the event will happen, (2) the magnitude of the event, and (3) none of the above. For this scenario to work there will never any information about where the event will happen. This must be a fixed point in the tachyon precursor.
By making it a galaxy wide detection allows everybody in the galaxy to be worried about an unspecified calamity coming somebody's way. Somewhere and somewhen in the galaxy and at ill-defined level.
The assumption has been made implicitly that the tachyon precursors are caused by an advanced type of weapon. Perhaps a typical piece of ancient alien weapons technology that can only be used once. That would add an element of surprise and uncertainty. This is unlike situations where weapons that generate tachyon precursors as a side-effect for their use are standard issue. On the other hand, this might not be the result of enemy action it could be a natural phenomenon.
Imagine regions of spacetime that undergo phase changes and emitting massive pulses of gamma radiation, high-energy particles, and the tachyon precursor. Some kind like an 'earthquake' happening in spacetime instead of a planet's mantle. There might be small pockets of false vacuum left over from the Big Bang. When these go pop tachyons are also emitted.
This does assume that the pockets of false vacuum aren't capable of destroying the universe. Although that might be one of the additional fears, that there could be a pocket of false vacuum powerful enough to take out the entire universe.
This answer sketches out some possibilities about a range of scenarios where tachyon precursors might be in play and how they might affect your characters. use this as a starting point to design the most effective scenario in your story. Good luck and have fun with it.