That's a good question with no real answer as the rules don't do a good enough job of defining these out of turn movements.
I would say that, from a strict rules as written literal interpretation, if you use an ability to move in the shooting phase, anything that mentions "the preceding movement phase" will not see that movement, but anything saying "if you didn't move" or something to that effect will.
Basically, if it calls out the phase explicitly, you can do movement shenanigans in non-movement phases with no drawbacks. If it mentions just moving, then out of phase shenanigans do count.
But also this is a moot point in regards to The Swarmlord because Hive Commander prevents shooting and the "instead of"
FAQ ruling explicitly calls out that you can only do it so long as you don't shoot.
Rulebook FAQ wrote:Q: Can abilities that are used ‘instead of shooting’, such as
Smoke Launchers, be used if the model using them has Fallen
Back, Advanced or has enemy models within 1" of it?
A: Yes. A model can use such an ability so long as it does
not shoot – it does not matter whether this is because the
model cannot shoot or it chooses not to.
Emphasis mine. This also means you cannot shoot with the Dakkafex first then use the Hive Commander to move it.