When a skill says 'damage based on', is that only what its based on? Or the damage type comes into consideration too?

Just wondering, as post update, I tried changing my magus allied soldier to all green talismans (as it now says damage scales based on max HP), but he didnt hit any harder. It would seem like, because its 'magic damage', it scales with magic damage as well as max HP...

Is this how you all understand it too?

Thanks!