The state is not required to have a theory in order to charge someone with murder and they are not required to stay tied to a theory they do have if the evidence they continue to uncover changes their understanding of an element of the crime. Only evidence to prove probable cause is needed for arrest and indictment and then of course at trial they need to convince a jury beyond a reasonable doubt.
In the Manson case, for instance, the whole "Helter Skelter" link, providing motive and context, was not uncovered or understood until long after the 3 girls and Manson were behind bars.
Motive is nice to have and juries always want to know, but motive is not a required element to obtain a conviction.
A theory is not required per se, but if the state can't put together a cohesive case that ties the evidence they do have together in a way that makes sense, then it will be hard for a jury to convict, so it's in their best interest to figure out the story they want to tell by the time the trial rolls around and of course make sure the evidence they do have fits that story.
In this case there is a pretty simple story: young woman sees man in her workplace, becomes attracted, pursues, he responds favorably, they begin an affair of some length (about 3 months), he's married, the wifey finds out, is furious/jealous/insertEmotionsHere, wants to control the outcome, threatens/harasses the mistress, probably threatens the husband, controls the husband's movements, continues to contact the mistress.... etc etc. In a way it's a very standard type of story with jealousy and revenge the likely motives on the part of the wife, and 'get rid of the problem once & for all' on the part of the husband.
