Getting extra units

I Know the AI gets bonus to build units and science. On Immortal, Continents plus, Huge.
I don't understand how they can get 25 units when i can only get 5 or 6.
Then while trying to defend my ally city state on a small island, 5 squares by 6, Iroquois was attacking from his city with four SAM. I surround the island with battleships on one side and destroyers and subs on the other, so i can see all squares, and no one can assist him from mainland.
I destroy 3 SAMS and leave one in the red.
Next turn he has three more SAMt and 1 rocket arty, takes the city.
I destroy the SAMs and liberate the city
Next turn he has 2 SAMs and 1 Rocket Arty.
He can buy one per turn, but where does he get 3 or 4?

The AI can move the units they buy immediately after buying and if I remember correctly they changed the AI-behaviour a while back, so they can now buy more than one unit, so I guess the AI may be allowed to buy more than 1 Unit per city/turn.

Another possibility would simply be airports. You can insta-teleport units between cities (and adjacent tiles) that have airports built in them although I've never seen an AI actually use them.

I believe ai have same rules as player on buying and moving. Ai does not cheat that way. (it has bonuses to production, grow, but ruleset is the same.)

Most likely paratroops in your case.

Yeah, I have seen the AI "appear" to get some unlikely number of units into a city all at once, but its probably just an airport when modern age or later.

unit Production ends: +1 unit
rush buy: +1 unit
airport airlift: +1 unit
paratroopers / XCOM :+X units (available tiles / #units in range)
? city state gift: +1 unit

In theory, all of these could happen at the same time, however unlikely
thats all I can think of.

I have personally dropped 5 XCOMS into a battle on one turn. the range on those things is silly.

I did not check for airport.. thought about it too late. captured the city and liberated it back to India, resurrecting him ( he voted for me in the UN , which gave me a win) Definitely not Xcom. I dropped six of them on his capital and took it in two turns.
Might have been there and just not showing. I've seen ships, especially, show only as a small icon with no flag.
Not a game breaker, just irritating.

The ai can get units overwhelmingly sometimes. If you take the honor social policy your units can promote easier and survive more if infantry.