[Soapy]

There are, to my knowledge, no talents or skills that increase tome power or decrease axe power.

Battle Objective: Defeat All Enemies - Defeat all enemies on the battlefield.
--- ROUND 0 ---
Hellion Hero's turn.
Hellion Hero's turn.
Hellion Hero's turn.
Jammer takes 106 Slash magical damage.
Status Infliction: 188.75 VS Status Resistance: 0
Jammer was inflicted with Burn!
The battle has ended.
Gained 1 Mura.
Battle Objective: Defeat All Enemies - Defeat all enemies on the battlefield.
--- ROUND 0 ---
Hellion Hero's turn.
Hellion Hero's turn.
Jammer takes 140 Slash magical damage.
Status Infliction: 188.75 VS Status Resistance: 0
Jammer was inflicted with Burn!
The battle has ended.

These numbers are with One-on-One, 59 Fire ATK, and roughly 97 SWA. Basic attack damage doesn't differ at all between Tome and Axe mode.

Based on that, if I had to guess, I'd say the skill isn't taking the 50% Fire ATK scaling into account when used in axe form for some reason.