Version 1.12.2-1.6.8

I've tried both Pam's Water Trap and Cyclic Automatic Fishing Net. Neither will catch any Aquaculture fish.

Pam's Water Trap has it's own set of fish that it uses.
Cyclic's Automatic Fishing Net only looks at what you can catch with the vanilla fishing rod.

It's indeed a issue with the mods fishing nets, as we inject it to the vanilla fishing table

Is it intentional that vanilla rod does not fish aquaculture fish? The modpack page says otherwise. Vanilla rod does not fish aquaculture fish. https://www.curseforge.com/minecraft/mc-mods/aquaculture

You're on 1.12.2, which is Aquaculture 1
The information you're reading about is for Aquaculture 2 (As stated at the top of the description, with Minecraft versions)
Close to the bottom of the description there is a spoiler with information for Aquaculture 1.
I didn't notice you were on 1.12.2 when responding before - fishing nets will indeed not work with Aquaculture 1 fish, unless it has special support

My response was for 1.12 I check the code for those versions of the mods.

Yes, but even if they did do things properly, it still wouldn't work with Aquaculture 1 at all.
(Accidentally reopened it before, oups)

Like I said before they have their own methods of getting the fish.
I'm linking the code for reference to both mods.
Pam's:
https://github.com/MatrexsVigil/harvestcraft/blob/master/src/main/java/com/pam/harvestcraft/tileentities/TileEntityWaterTrap.java#L211
Cyclic:
https://github.com/Lothrazar/Cyclic/blob/trunk/1.12/src/main/java/com/lothrazar/cyclicmagic/block/fishing/TileEntityFishing.java#L198