I resolve it through accurate roleplay. Regardless of the Initiative number, a player should play their character. A combat vet and a person who have never seen violence in real life will react very differently. In a case where initiative is unclear, I always default to roleplay. If I am playing the non-combatant and I win Initiative, I am likely spending My first round panicking. Maybe My second round running for cover or some such. By round 3 someone might have reminded Me that I have a weapon and to shoot back. I play like this no matter the Initiative roll, so maybe this won't help you mechanically. Initiative is only reaction time, nothing else. If you freeze in combat, that isn't usually a function of initiative, unless you rolled really, really badly, it is a function of lack of experience. Both parties may react at the same time, but their actions will be vastly different. This is something that isn't covered by the rules and I am not sure that determining player actions should be covered by the rules. Trained combatants will engage the enemy or fall back to cover or both or a number of other smart, effective things. The non-combatants, well, they won't. This is less of a mechanical thing than a roleplay thing in My games. That is why in My games, using the Recon skill as an Initiative roll works well for Us. Recon tells you how quickly you notice the problem, then it is up to the player to roleplay if their character takes effective action or ineffective "panic" actions. Granted this requires you to have gamers at your table that will act against their character's best interests in the interest of roleplay instead of roll play.
For example, I tend to "power game" My stats and skills, but I use them in ways that often counterbalance them. He will take actions that make sense for the character but do not use his abilities in a smart way from an OOC perspective. For example. Perhaps a combat vet with PTSD. Great stats. Great abilities. The choices I make for the character are not always great from a succeeding or surviving point of view. When it is needed to save the party from multiple character deaths, sure, I may use My stats and abilities intelligently, but mostly I just play the character.
Or an amusing example is Fizban from Weis and Hickman's books. Very powerful, but not very useful, or of limited use anyhow.