I cannot be sure without seeing the entire map, but from your screenshot, I have a feeling these are brand-new units built by the AI which were expelled to your territory because they have no other room to be placed on. Notice how they appear only on the west side, not in the middle of your territory.
The principle is simple: if the AI is supposed to get a new unit, but that unit has no room to spawn in, OR if the tile the unit is on suddenly became inaccessible to the unit (e.g. it was conquered by you and you have no open borders agreement and are not in war), then it is instead transferred to the closest available land tile. Looking at the west side of your map it's all mountains and ocean, non-accessible for non-helicopter ground units.
Here's an example of this happening to one of my units:
![icebound unit](https://i.stack.imgur.com/rg94K.png)
There's absolutely no way for infantry to get to that tile, but this unit did because it needed to spawn or move, and this was the closest available tile for it to move it.
In addition, keep in mind that in high difficulties the AI gets significant discount on both unit build cost and unit maintenance, which allows the AI to field a huge military that can indeed fill up its continent - here's a sample from a game I had in an easier difficulty than yours:
![tons of units](https://i.stack.imgur.com/0rgRC.png)
So I have a feeling this is what happened here. As far as I know, other than paratroopers, this is the only way a unit can magically teleport into your continent in the way you have described.
I can't think of any simple way to solve it other than killing some of the units parked in the enemy's continent.
Best Answer
The location of the antiquity site determines what civilization the resulting artifact is from. If you only work antiquity sites within your borders, you'll generally get artifacts from your civilization and barbarians. If your territory includes conquered cities, sites from that part of your civ could include artifacts from that civ.
Once an Archaeologist has worked an antiquity site, the civ that worked the site gets the artifact and the site disappears, regardless of the location of the site. So if an AI works an antiquity site within your borders, they get the artifact instead of you.
Working an antiquity site within the borders of another civ will trigger a diplomatic warning from the AI. You can tell them that you'll stop working sites within their borders, or ignore their warning.
I try to strike a good mix of working antiquity sites within my borders, in unclaimed territory, and also within other civ's borders (as I am able to do with open border agreements). This helps to give me as many options as possible for theming bonuses.