The Rakshasa has the Limited Magic Immunity trait:
Limited Magic Immunity. The rakshasa can't be affected or detected by spells of 6th level or lower unless it wishes to be. [...]
As noted in this Q&A about its interaction with the UA Revived Rogue's Bolts from the Grave feature, the Rakshasa can be affected by Bolts from the Grave because this source of damage is not a spell, but rather a class feature.
It appears that the Rakshasa can also be affected by the paladin's Divine Smite feature, whose description says (emphasis mine):
Starting at 2nd level, when you hit a creature with a melee weapon attack, you can expend one spell slot to deal radiant damage to the target, in addition to the weapon’s damage.
Even though the feature is powered by spell slots, it is not a spell; it is a class feature. The radiant damage is in addition to the (nonmagical) weapon damage, which seems like it is not part of the weapon damage itself.
Beginning at 10th level, you can add your Intelligence modifier (minimum of +1) to one damage roll of any wizard evocation spell that you cast.
Suppose an Evoker of 10th level or higher targeted a Rakshasa with an evocation spell of 6th level or lower: the Rakshasa would be immune to the damage from the spell itself.
But the damage addition from the Empowered Evocation is not from the spell; like the Divine Smite, it is from a class feature, which argues for it not counting for the immunity.
The two features use similar language to describe this damage; 'added to' vs. 'in addition to'. I don't think either term is a game term, and there is considerable overlap between their natural use in English.
One clear difference between the two is that the type of damage for Divine Smite will typically be different for the Smite than for the weapon - unless the weapon itself is doing radiant damage. Whereas for the Empowered Evocation, the empowered damage will typically be the same as the damage type of the spell, although this has exceptions as well.
Another difference is that Divine Smite adds 'dice' of damage while Empowered Evocation adds a static modifier.
Is 'usually similar damage type' enough to rule that the Empowered Evocation just increases the damage to which the Rakshasa is already immune? Is the distinction between 'added to' and 'in addition to' important enough for the answer to turn on that? Does it matter that one damage is determined by a roll and the other not?
Is the damage from Empowered Evocation a separate source of damage, to which the Rakshasa is not immune? Or does it simply add to the existing spell damage, so that now there is a bigger pile of damage to which the Rakshasa is immune?
A good answer will not only respond with a ruling, but will explain which of these factors are important and which are not in considering the ruling.