Here are two principles:
(1) The universe is very finely tuned. There are a bunch of numbers programmed into the laws of physics, like the speed of light, masses and charges of the fundamental particles, Plank's constant, Newton's constant, and the fine structure constant. The fine structure constant for example is related to how strong of a pull charges exert on each other.
You can imagine tweaking any of these, and all that happens is that everything gets a bit heavier, or maybe magnets get a bit stronger or weaker. The hard part is tweaking things like this makes atoms either unstable or makes them collapse entirely. So you end up with a universe with no complex matter. Just a bunch of high energy particles whizzing off everywhere.
(2) There is a finite list of "allowed particles". If you shoot a bunch of lazer beans into each other then you get a large concentration of energy at a point. The universe has to decide what to do with this energy. Some of it will get turned into particles and some will get turned into the kinetic energy of those particles. If you shoot enough lazers you might get some electrons popping out. If you shoot even more you might get some protons or Higgs bosons or some other heavier particles. But you cannot shoot a small amount of lazers to generate half an electron.
Now its concievable there is a different universe with different constants that makes complicated matter possible but the rules for how it behaves and list of allowed particles is different. They have atoms but their atoms are different.
I imagine someone has a chunk of matter matter from the other universe in a time suspension field and loads of scientists looking at it going "this isn't allowed". Then someone accidentally turns off the field; the rules for our universe kick in, realize the particles in the contained are not allowed. But the particles still have energy due to having mass and that whole $e=mc^2$ mumbo jumbo that hardly anyone every talks about. Since the energy has to go somewhere it gets converted into a bunch of smaller allowed particles that go whizzing off in all directions. Boom.
Would it be possible that it "retains" the physics from it's universe of origin etc?
We like to think there is a big proton field that underlies all of time and space, and a proton is just a little wibbly wobbly bump in that field. Likewise there is an electron field and photon field, and so on for all the fundamantal particles.
If the second universe has an electron field but that field is a bit slower so they exert less of a force on each other, we can imagine the second electron field wobblying into the first one and producing ripples (particles). Then the particles are in our field and would obey our laws.
Imagine some sound waves are moving through water (where they move slowly) and then travel into a solid (where they move faster). The waves were created in the water perhaps but they don't remember that fact, and as long as they are in the solid they follow the physics there.
Now if the second universe has some other X field that we don't have then it's hard to imagine how some X particles could even exist in our universe at all. You could imagine their X field bangs against our photon field and creates a bunch of photons. But I don't think that's exactly what you're looking for.
Or maybe we DO have an X field but for some reason there is no way to actually stir it up and create X particles? We can only get them from the other universe. This might be your best bet. . . I am not aware of anything in physics that specifically FORBIDS an extra field that is there but doesn't actually do anything.
Or am I free to totally make up how it acts and effects and interacts with our universe?
I'd say you are totally free to make up whatever happens at the boundary where the matter passes from one universe into another. But if you start saying the alien matter follows different rules to ours, once it's inside our universe, then you'll get loads of physics curmudegons like myself who cluck their tongues, stroke their beards, and talk about "What's to be done with this Homer Simpson?"!