Question regarding Battlemage's Cry

Hello Exiles,

i currently thinking about the new Battlemage Cry Skill.
It says "Buff Makes Increases and Reductions to Spell Damage also Apply to Attacks.. bla bla bla".
Since the PoE Tooltip is not always the best Source i'm having a few questions if these sources are added to my attacks or not.

Pain Attunement - 30% more Spell Damage on Low Life (yes/no?)
Wrath - 15% more Spell Lightning Damage (do this also affect Lightning Attacks?)
Added Spell Damage (for example Abyss Jewel 7 to 11 Added Spell Cold Damage while holding a Shield ) (yes/no?)

In PoE Tooltip there are no changes at all for any of these sources so i'm kinda struggling with my plans for the next build.

only mods that literally say "increased spell damage"

in PoE "increased" is a specific term, not generic one