Rem Karolus, Stalwart Slayer

The additional 1 damage is dealt by the original source of damage. The additional damage isn't dealt by Rem Karolus.

If damage dealt by a source you control is being divided or assigned among multiple permanents an opponent controls or among an opponent and one or more permanents they control, divide the original amount before adding 1. For example, if you cast a spell that deals 4 damage divided among any number of targets and you choose to have it deal 2 damage to a creature and 2 damage to that creature's controller, that spell will deal 3 damage to each of them instead.

Rem Karolus, Stalwart Slayer's last two abilities apply only to damage dealt by spells on the stack. A spell that becomes a permanent and then deals damage won't be affected.