From what I can tell, there are three types of damage that's affected by BLM's Manaward/Manawall. One is physical, which is blocked by Manawall, as you've mentioned. A second is magical, blocked by Manaward. And there's a 3rd type that isn't blocked by anything (Earthen Fury, Hellfire, Aerial Blast). However, you seem to think that the damage type is linked to whether the damage is physical or magical, but I would disagree.

Most physical attacks can be blocked/parried/dodged, but magical attacks cannot be, or maybe it's a property of the attack. So, you know that Twintania's fireball is a magical attack based on it being fully absorbed by Manaward, but I know you can definitely parry it. So it doesn't really make sense that it can be parried as a magical attack. Likewise, in PvP, I can't expect a tank to block or parry Fire I nukes from a BLM. So there might be some other factors in determining if a skill is affected by STR/DEX or INT. I don't believe Manaward/Manawall is a good litmus test.

At least if you're doing Titan Extreme, it's pretty easy to test the early tumult damage, since not much is going on during that phase. Lastly, don't forget that Paladins automatically have a -10% STR debuff.