In Pathfinder 2, is non-physical damage calculated separately from physical damage for a single attack?

One of the players in my game is playing a dragon instinct barbarian. The GM is calculating the elemental damage separately from the weapon damage for resistance purposes (i.e. an axe attack deals 8 slashing and 4 cold, which is broken into two different damage groups.) Is this correct, or should this be counted as a single group (12 damage)?

Draconic Rage (Instinct Ability) While raging, you can increase the additional damage from Rage from 2 to 4 and change its damage type to match that of your dragon’s breath weapon instead of the damage type for your weapon or unarmed attack. If you do this, your Rage action gains the arcane and evocation traits, as well as the trait matching the damage type.

Dragon Instinct: