These are two very different concepts that you are relating here. A Lorentz boost can transform a tachyon into one seemingly moving backward in time because the

These are two very different concepts that you are relating here. A Lorentz boost can transform a tachyon into one seemingly moving backward in time because the tachyon already travelled on an (unphysical) space-like trajectory. In special relativity, any space-like trajectory has no causal order of events, so this is more of a statement how much tachyons would screw up the world of physics if they were real. The paper argues that this can be kind of remedied by introducing a dual space, but this is not relevant here. In Feynman diagrams, all particles travel on time-like (i.e. physical) trajectories. Well, technically not, but there is a fundamental mechanism that cancels out any space-like propagator components. But let's not get into that. Back on topic: there is this neat property of quantum field theory (known as CPT symmetry) that says a positron behaves like an electron moving backwards. This is why you usually see arrows denoting anti-particles pointing back in time. But this doesn't mean that anything is actually travelling backward in time. It just makes certain calculations more tractable because of the way field operators are ordered, but there is nothing fundamentally weird about it like for tachyons.