I still pop in from time to time and try to answer questions quickly. I have other plugins in the works, but I've been dealing with life.
For making battlers talk during skill animations, you must be using Yanfly's Action Sequences (I presume you are). Let me give you an example from the current build of Jay's Journey.
In Jay's info box, I have the following defined:
<voices> ... attack|VXJayAttack1 attack|VXJayAttack2 ... </voices>
(If it's unclear, the "..." just means "I'm skipping stuff here.")
Then, in the action sequence for the basic Attack skill, I have an Action Sequence that includes:
<Target Action> ... FACE user: target VOICE user: attack MOTION ATTACK: user ... </Target Action>
The "VOICE user" is the magic. When it reaches this point in the action sequence, it will look to see if the skill's user has any voice clips labeled "attack". Jay actually has two, as you can see above, so when he attacks it will pick one of the two at random and play either the sound clip "VXJayAttack1" or "VXJayAttack2".
For the spell "Health", I have the following:
<Whole Action> ... WAIT FOR ANIMATION VOICE user: target, health MOTION SPELL: user ... </Whole Action>
"target" actually looks for an "actor#" or "enemy#" tag, depending on who the target of the skill is. So if Jay was casting Health on Carol (actor 2 in the database), it would collect all voice clips labeled "actor2" (and all voice clips labeled "health") that Jay has defined and play one at random. (And none of what's in the action sequences is unique to Jay. If another character uses basic attacks or the Health spell, their own voice list will be referenced to determine what voice clips play.)
Do you get the basics?
I don't know how Olivia's Victory UI works (I'm using Yanfly's Victory Aftermath instead), but I can guess why they'd interfere with each other where it comes to the ends of battles. I don't know why they'd interfere with each other outside that. If you bring up the debugger (press F9 in "Playtest" mode) do you see any red text while both are active?