Right, each AI has their own waves. So one sends them, the other doesn't.
In terms of those steady streams of ships, you will indeed run into that sort of thing... sort of. It won't be in the form of a small stream, but the AI will "stalk you" for a while, and then suddenly bust in out of nowhere when it feels it has superior force. If you don't take a turret-happy approach like you were doing, then on higher difficulties you will die. It's just at the lower difficulties, and on some specific maps, where you might not need as many -- but even then, if the AI gets a breakaway force, and you have no turrets, you're screwed then, too. So it's a matter of maintaining some defense-in-depth, which is key.
In past versions even in the regular game the AI would trickle in. However, in recent versions I taught it a new "stalking" behavior where it waits until it thinks it can win with its forces before it comes in. So that leads to more "occasional gushes" rather than "continual trickles." The turrets, in that sense, act as a critical deterrent, too.
And so I can make sure I now understand this correctly: The only things that are going to cause the AI to cross a border and attack my worlds (outside of specific ships or guard posts with special abilities) are going to be me 'pulling aggro' by poking my nose in to their planet, or the specifically announced waves from warp gates, right? If I move in to the planet next door but never send anything to their side of the fence, I can safely assume ships aren't just going to randomly trickle in for no specific reason?
No, there's way more than that. The sources of ships are:
1. Special Forces ships (they wander around all the time and will randomly pop in -- on anything higher than I think diff 5).
2. "Threat" ships in general can come in at any time. Read up on the wiki on these, but ships that are freed from your "pulling aggro" or doing whatever else count as this, and they can be spawned in a few other ways. AI ships will often retreat from battle and then lurk as threat, too. Not on the lower diffs, though. These are the ships that will stalk you and then suddenly come back in.
3. Waves are those periodic, announced things that come directly into your planets.
4. Cross Planet Attacks will get announced every so often, and then after about 12+ minutes you'll have probably a few thousand ships all go threat at once.
5. As planets reinforce a ton, they will first create a barracks, and then start creating carriers, with the overflow. The carriers are like AI transports, and they'll count as threat and stalk you in the same way.
6. As planets reinforce a ton, they will also start having "border aggression," where small numbers of their ships will trickle out of their guard status into threat. These ships then join the others in doing... whatever they think is best.
7. Obviously, if you opt to turn on some of the minor factions, they have all kinds of crazy behaviors. The hybrids are the most brutal out of them, but there are many various flavors of sub-factions with different behaviors.
There are also some more edge cases, but those are the main ones. The wiki has more info on a lot of that, if you want all the details on each one. Or you can opt to just discover as you go. Bear in mind that if you were playing below difficulty 5, it's really not including the full range of the AI behaviors, not even close. Once you move up to 5 it's a bit closer, 6 is a lot closer, and 7 has about 97% of them. Diff 8 is where
absolutely 100% of them are, and it's extremely difficult as well.
In a lot of senses the tutorial is training you for the higher difficulties, so indeed it might be overkill if you play that way on the lower ones. But, to some extent it's better to be safe than sorry, eh? I can't count the number of games I've lost because I was fighting the AI on planet A, and then they broke through my defenses and skipped through other planets without my noticing, only to kill my homeworld. Having automated turret setups at key junctures can really help with that (though it won't prevent it entirely, with things like starships and guardians).