Perhaps having 'boundary events' for territories would help? While I agree that a dinosaur probably doesn't need to be committing ultra-murder, these are living animals that get curious, and if there's a sudden change in the territory then dinosaurs taking the time to investigate would probably be of interest.
It might go like this-
-You make a change to the enclosure. For example, there's a new feeder, or a new species gets airlifted in, or you've added a new guest attraction to the fence, or a fence becomes damaged or broken or turns off.
-A secret alert is made. One of the dinosaurs whose territory overlaps, or one of the dinosaurs nearby, or some other method selects a dinosaur, which is 'informed' of the secret alert. That dinosaur will wander over when it's not busy, or another dinosaur will wander into the alert and take it for itself.
-When a dinosaur reaches the secret alert, it will take action to investigate it. Different dinosaurs might different responses based broadly on their category and certain traits- large carnivores might attack tour vehicles out of curiosity, small dinosaurs might follow around a larger animal to size it up, alphas or social animals might call the rest of their group, skittish dinosaurs might panic, and any dinosaur might challenge a disliked dinosaur or leave through an unexpected hole in the fence.
And to provide an example of how it might work in practice-
-You have a pack of 6 velociraptors, who are all casually chilling being velociraptors. They are living with 3 euoplocephalus, who are grumpy about having to share with the raptors but who are too bony for the raptors to make any legitimate efforts to kill them. The enclosure is very large, so the two groups tend to be in different areas from each other at different times.
-You divert a tour through the enclosure. One of the raptors is selected to investigate the entry gate, and another raptor is selected to investigate the exit gate.
-The entry raptor has the Aggressive, Intolerant or Intelligent trait, and so it selects an 'ambush' behaviour to see if anything will happen for it to attack or scream at. The exit raptor gets hungry, gets in a fight and goes to sleep before it does anything, but none of the other dinosaurs stumble into the exit gate, so after a while it heads over and uses the 'call pack' behaviour because it's Social or the Alpha. Others raptors arrive; some of them wander off, some of them select ambush behaviours like the first raptor, and some of them select gawking behaviours where they'll just wander back and forth and bark at the new thing for a while.
-A tour jeep arrives, but the first raptor has gotten hungry and wandered off. However, there's still a raptor waiting in ambush at the exit gate, and so the tour jeep gets attacked.
-Later, an unhappy employee causes a fence opening. Two gates in the enclosure open. Both alerts target a Euoplocephalus, but they're both socialising.
-While they socialise, one of the raptors walks into the alert area for an open gate, and takes over the alert. Being a Tolerant small carnivore, it activates the 'escape: zoomies' behaviour, where it'll activate an alert for the rest of the raptors to launch their own investigations and spends some time running around like a maniac until it's interrupted or decides it needs to hunt. Other raptors activate the 'escape: rampage' (where they'll go murder things instead of just running around making a nuisance of themselves) or 'escape: zoomies' behaviours when they arrive at the beckoning of their packmate.
-One of the Euoplocephalus is still being summoned, as none of the raptors noticed the other gate due to being distracted by the first, and walks up to it. This Euoplocephalus decides on the 'escape: traffic jam' behaviour, being an armoured herbivore, and summons its herdmates while it finds the busiest path or tour in the local vicinity, sits down on it, and deactivates its panic aura. One herdmate sees all the humans staring at the other euoplo and decides on the 'escape: panic' behaviour, where it'll run away from humans and has a chance to break down fences (see: Prehistoric Park's titanosaur rampage), while the other decides on the 'escape: passive' behaviour- it wouldn't have summoned anything if it had been the first out, and while it won't actively run amok like the rest of the dinosaurs who've gotten out, it will preferentially go for resources outside of the enclosure rather than inside of them.
I think a system like this, which can convince dinosaurs to make nuisances of themselves without having to make them set behaviours, would be very useful for making escapes feel more important and likely. Particularly for herbivores; they're really not much of a nuisance to deal with even when they do escape, and having a chance of your herbivores causing a chain reaction by panicking and attacking other fences would make it worthwhile to invest in sturdier exhibits for herbivores!
it's not that hard. Accidental Dino scapes are the main plot of the jurassic park films, so... not wanting accidental scapes it in a Jurassic Park game its pretty confussing to me
