In special relativity the space-time can be seen as a static four-dimensional picture that contains the entire past and the future of a flat universe. And the patterns in it are subject to several constraints to make it physically feasible. Observers within it observe it by sweeping their plane of simultaneity through it. In this case anything that moved faster than the speed of light would draw a space-like line through spacetime.
And one doesn't even need to have tachyons to have a space-like line of events. For example it's possible to flash a ribbon of lights simultaneously, which can draw a similar space-like line of events. And observers wouldn't notice anything special other than just a regular line of space-like events.
Would tachyons be any different than just a ribbon light flashed simultaneously in a frame of reference?