That’s the interpretation that makes sense, yes.

Since there is no demarcation between fluff and crunch in spells, the whole spell effect is rules. The effect says that it lessens the effect of the triggering damage; when you wonder “how?”, the effect supplies the answer: you have resistance.

D&D 5e is somewhat resistant to fine-grained timing analyses, and doesn’t appear to try to nail down a precise tick-by-tick ordering to things that could be resolved simply by the DM saying, “Yes, it does what it says on the tin.” Since any other interpretation makes the spell not do what its effect says it does, the interpretation that lacks internal contradiction is the correct one.

If it helps, Jeremy Crawford has tweeted about this, once:

Q: Does Absorb Elements give you resistance to damage from the triggering attack?

A: Yes.

And twice:

Q: When someone casts Absorb Elements, does he take full damage from the attack he is reacting to?

A: The absorb elements spell works against the spell that triggers it.