Hmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm so this changes things slightly.
If alluka has different personalities only around killua that means it's possible that her power is separated like this. She doesn't pester her parents because she doesn't want them to die. So why does she pester killua, yet killua knows that when she calls him by different names it's a different person. Illumi mentions that if killua does a pestering, but lies, bad s'hit will happen, so the fact that nothing bad happened when killua faked his death in this chapter means that alluka when referring to killua as onii-chan has no activation of her ability in any way. She just wants to play with her brother...i wonder if this has any effect on the lessening of her pesterings.