I have heard from my Rav and during a few derashot of HaRav Eliyahu Mansour that a neshamah previously brought into 'Olam HaZeh in human form, but needing additional tiqqun (i.e. soul correction) and no longer being able to achieve such tiqqun in human form (HaRav Mansour recently quoted an opinion that a neshamah can descend in human form a maximum of three times), can return to This World in other forms (i.e. animal, plant or inanimate form).
I'm no mequbal (i.e. Qabbalist); but, assuming my understanding above is correct, does that mean that every non-human creation is necessarily a gilgul (i.e. reincarnation) of a neshamah that was previously brought into This World in human form?
While it's true that some animals, plants ... are gilgulim of people, that does not mean that all are. Reincarnation is usually because a soul has to fix something it did or did not do but for whatever reason can't go to gehinom or needs to be done in the physical world. Most souls however either throughout the course of their life completed what they needed and are able to be cleansed in gehinom of whatever impurities they may have picked up.
Also to clarify there are 2 concepts The return of a soul into a new body which happens quite often and the "piggybacking" of a soul into a body human or otherwise that already has a soul.(similar but not the same as a dibbuk). This is what you asked about(As well there is the resurrection of the dead by the times of mosiach). In the case of the return of a soul, the soul I the person having full control over the actions of he person. Whereas by piggybacking the soul while it may provide some benefit to the body it inhabits (such as I think leaders get assistance from moshe rabeinu because a "piece" of his soul goes into their body) it does not have control over the person (unless of course it's a dibbuk) for sources see discussion about moshe rabeinu and yakov avinu an how Kabbalah explains the phrases moshe lo meis (Moshe did not die) and yakov lo meis. As well there is shar hagilgulim in eitz Chaim by R Chaim vital which should have everything.