There seems to be something wrong with my set-up when trying to use a mod that modifies leveled lists. Other mods I've used work just fine (like a mod that removes the helmet requirement for armor perks, and a couple graphic tweaks, etc.). But for any mod I've attempted to use that adds things to leveled lists like merchant containers, enemy spawns, chests, etc., the changes to the leveled lists do not actually occur.

Case in point, Immersive Armors. This mod adds many new armor items into the game. After playing for weeks after installing it, I've yet to see any new armor. Except for a set called Hunter Armor, which according to the Mod Description is manually added to certain NPCs. And I can also get them with the console. I can't blame Immersive Armors for this, because I've had the same issue with other mods.

Is there a basic mistake I'm making? I'm relatively new to mods in Skyrim, but I'm a ninja with Oblivion mods so it's all familiar.

If it matters, I'm starting Skyrim with the SKSE Launcher via Nexus Mod Manager every time. Any ideas would be greatly appreciated

Are you using a bashed patch to merge your LL's? Otherwise, you'll only get LL changes from the last mod installed.
If you are, have you tried disabling the patch and testing? (I haven't heard of any problems with bashed patches, but you never know)

For the past month, I've only had one mod that changes LLs, so I never worried about bashing.

I would suggest you try it. Couldn't hurt? If you're still not getting IA's loot to show up then perhaps you'll need to investigate that mod a little more.

Maybe you're simply not high level enough?

Level 25.

Yeah, well, check in the Creation Kit at which level the items should appear. What's your game version?

I'd have to check, but I update it (and SKSE) with each automatic Steam update.