Does Empowered Spell metamagic work over multiple turns?


The Sorcerer’s Empowered Spell metamagic option reads

Empowered Spell When you roll damage for a spell, you can spend 1 sorcery point to reroll a number of the damage dice up to your Charisma modifier (minimum of one). You must use the new rolls.

While the spell Immolation reads (emphasis added):

Flames wreathe one creature you can see within range. The target must make a Dexterity saving throw. It takes 8d6 fire damage on a failed save, or half as much damage on a successful one. On a failed save, the target also burns for the spell’s duration. The burning target sheds bright light in a 30-foot radius and dim light for an additional 30 feet. At the end of each of its turns, the target repeats the saving throw. It takes 4d6 fire damage on a failed save, and the spell ends on a successful one. These magical flames can’t be extinguished by nonmagical means.

If a sorcerer with +5 CHA uses Empowered Spell on Immolation to re-roll 3 of the 8d6 and the target fails its save on its next turn can the Sorcerer re-roll an additional 2 dice of the 4d6 damage?

This question might include whether Empowered spell should be read as:

"When you roll damage for a spell, you can spend 1 sorcery point to reroll a number of the damage dice [from that damage roll] up to your Charisma modifier"
or
"When you roll damage for a spell, you can spend 1 sorcery point to reroll a number of the damage dice [for that spell] up to your Charisma modifier"