" Is it absolutely necessary to have a dissociative disorder to have trauma?" No. But it is probable that there was trauma if you have a dissociative disorder or you wouldn't "need" one.

Disorders of any sort generally come from trauma of some sort. Whether it was by one's parents/care givers or not is neither here nor there and what opinion we have of our parents/care givers and childhood does not necessarily tell whether they were abusive or not, just what we think/feel. People lie, cheat, or steal to keep from having to admit they were abused and some people who know they were abused will lie, cheat, or steal to keep from having to admit they have a mental disorder.