The first thing you must do is give that lovely kitty a smooch on the nose from me!
Remove the plastic wrappings from the little trees. Look at the bottoms of the pots. Do you see any little root tips emerging from the drainage holes? If not, then the situation is not urgent. All will be well for at least a week, quite possibly longer, so you have plenty of time to evaluate things and plan your approach.
Those look like 2" pots. Is that about right? If you see roots emerging from the drain holes, you will want to repot them, but I would wait a couple more weeks before I did that.
Select a pot that is about one size larger than the ones the trees are currently in. I would choose a 4-inch pot, I think.
When it comes time to repot the trees, you will need a potting mix that drains rapidly and doesn't hold too much moisture, so avoid those with a lot of peat moss. If you aren't able to find anything like that, then you'll have to add some coco fiber or perlite. (Coco fiber is also known as coir.) Combine 2 parts of the potting mix to 1 part of the coco fiber or perlite.
Before we get into the details of repotting your trees, let's assume that they're going to be fine in the pots they're in, for awhile at least. Give them at least 6 to 8 hours of direct sunlight a day. If you can't provide that, then you'll have to supplement with a grow light.
Allow the soil to dry slightly between waterings. Give them enough water so that the excess runs out the bottom of the pot. Don't allow water to remain the the drainage tray or saucer.
They need high humidity, so you might want to place them on a humidity tray, which is just a tray filled with pebbles. Add enough water to fill the tray to just below the surface of the pebbles. You don't want the pot touching the water surface. The diameter of the tray should be at least as wide as the widest part of the tree. An alternative is to mist the plant with water several times a day, but I find that too messy. Also, I feel that a humidity tray provides a more constant source of humidity around the leaves.
Now, tell me about the root situation.
"Isn't it enough to see that a garden is beautiful without having to believe that there are fairies at the bottom of it too?" - Douglas Adams