Okay, so I've taken a close look at this and as crazy as it seems - this would be the expected result of how these two skills behave, and I would not consider this to be a bug.
What it comes down to is - if the basher terrain check finds no terrain, the basher stops on the spot (indeed, a fencer would behave the same way too). Because the lemming hasn't moved forward, it is in midair when the basher is assigned. However, no "is there terrain below me?" check occurs until after movement. I would absolutely agree that this is weird, and that in hindsight, the basher - and most skills for that matter - should revert to faller the moment they have no ground below them, just like blockers do. However, this detail itself - that some skills can operate in midair until a certain point - is far too ingrained by now to consider changing. Now, the difference with the miner occurs because the miner has no terrain check other than "am I standing on something?" (which, like the basher, doesn't get checked until after moving). One particular thing to note here: If the basher terrain check does find terrain, and thus the basher continues, he will continue through, just like the miner.
I'd certainly handle all these cases differently if I were designing a new engine from scratch, but for NeoLemmix, these are far too ingrained to change now. And in light of the above - this is an expected, if weird, behaviour, and not a bug.