It's true that the data in the game is random but there are factors! The most known is the season in your hemisphere. It'll affect which fish/insect are available. I'm not sure if it's luck, but I do notice that some times I catch better fish on a friends island. But it's not way guaranteed or does it apply to any of the other islands I've visited. But, for reference we know that large fishes in your River mouth (where ocean an river canal/end meet) that you'll catch a sturgeon almost all the time if the shadow is long/large. I think it's amazing you've caught what you did!
On a side note, unless you invest in NMT (Nook Miles Tickets), these mystery islands have specific island fish/insect varieties which CAN be special and spawn rare fish/insect. The opposite can be said about Kapp'N islands which are not concrete in fish/insect spawning, but depending on the day you might get a shark or see a fin sticking out in the water.
Just a gentle FYI, you have your information backwards about Kapp'n and mystery islands. But first, to clarify, critter spawns are determined by their availability period (aka current date and time), physical location on the island (e.g., clifftop vs. non-clifftop), flower availability and color, your hemisphere, the weather conditions, and catch locks*.
There are 11 types of Kapp'n islands. 3 of these islands' date and time will always match your home island, which means the critters you can catch there are always going to be the
exact same as the ones on your home island. These islands are the vegetable island, the gyroid island, and the "plain" island. The remaining 8 islands all have specific date and times that they are always set to, as detailed in the image below, which allows the player to catch critters that are not necessarily "in season" on their home island. [
Source]
Conversely, mystery islands you visit by using Nook Miles Tickets will
always match your home island's date and time, meaning the critters you can catch are
always the exact same as the ones you can catch on your home island.
TL;DR, critter spawns do not depend on anything that is unique to your island. To my knowledge the only thing that is unique to each island is the weather seed. I hope this helps!
*A
Catch Lock is an internal number specified by the game that prevents certain, often rarer, critters from spawning until you catch a certain amount of that type of critter. For example, the coelacanth
will not spawn until you have caught 100 fish in the lifespan of your game, even if the other conditions to spawn (correct day and time, correct weather condition) have been met. Only some critters have a catch lock.
