You are correct. Some seem confused or misinformed about the nature of what is allowable evidence in the punishment phase of a trial.
When it comes time for deciding how long an AK sentence is to run, there is a wide range of possibles, from 5 years to 99 years. So how is it decided? The largest part of that will be determined by the details of the totality of the crime itself, and the perp's actions. Did he mitigate his crime, or did he exacerbate it? What sort of ramifications did it have, and what did he do (or not do) to make it better or worse? All of such items are things clearly relevant to the case itself, and many of them are in the testimony in the case-in-chief rather than in the punishment phase.
But beyond that, both sides are allowed to present "irrelevant to THIS case" testimony that bears on the character of this defendant.
From the state, what other things of an illegal nature is he doing, or has he done? Those may be completely different types of crime, but the presence or absence of such things shows an attitude towards following the law. Is he a moral upstanding person, or a pervy sleazeball who is obsessed with illegal and deviant things and perhaps likely to play them out? Some of those may not even be criminal, but it reveals mindset and likely propensity to do this crime or that in the future.
In this case, the state wanted to show some linkage between the "otherwise irrelevant acts" and the actions of EA to CM, which would further bolster an argument over how heinous this crime was. But the acts themselves were allowable, relevant or not, and it's up to the judge or jury to decide if you can connect the dots further.
On the other hand, the defense is allowed to show things that might excuse the perp somewhat, even if not relevant to the crime. Is he charitable to others, was he a victim of abuse when young, did he have a hard time with this or that and have to overcome it in life, is he the type of person that would make a positive impact on the community if he was released and out on the streets, are there people who would be positively benefited by him serving a shorter sentence (say, for example, a family member or friend that he generously supports and cares for)? Does his life pattern show a propensity to follow the law, where it's unlikely that he would get out and do something bad and force the state to do another trial and lock him up again?
Much evidence against him, None in his favor. With a life sentence possible, no reason to ever want to let him out again, where he can be free to do something again, or worse.