There isn't a bug here; at worst, there's a mechanic that should maybe be changed (but I'm not entirely sure if it should).
How the nuking works is, immediately after the nuke is activated, lemming #0 starts counting down. The next frame, lemming #1 starts counting down, and so on. If, for example, lemming #1 no longer exists (due to, in this case, exiting), it doens't immediately proceed to lemming #2, but rather, does nothing on that frame (and on the next frame, lemming #2 starts counting down). Note that this behaviour is unchanged from vanilla Lemmix.
In Insane 16, the climber you mention is lemming #191, so almost the last lemming to start counting down. Because he's isolated from the crowd at this point, it's very noticable, but there's actually nothing unusual happening here. Since a countdown for nuking lasts 85 frames, plus the 16 frames of ohnoing, this means that by the time he even starts counting down, 90 lemmings (give or take one) will have already exploded if they didn't exit before this; and likely, many more will have exited mid-countdown or even mid-ohno.
Even if the behaviour was changed to skip removed lemmings rather than having a do-nothing frame, it's likely that you'd still get a similar effect on this level due to that many more would have started counting down, but exited before they explode.