If I'm the active player, and I'm in the Realm Phase, and my opponent plays an Action that deals 2 indirect damage to both, who assigns first the damage? It should be me who are the active player, right?

That is correct.

Thank for the prompt reply Mallumo.

Horatius said:

The damage is technically all assigned at the same time, but as Mallumo said, the active player is the one who makes the decision first.

Yes, it is true that the damage is contemporary, but I wanted a confirm who was the active player the first who choose how to allocate the damage, regardless of who is who inflicts the indirect damage.
This is especially important when you have in play units with "Savage" and "Redirect the damage"

Thanks Entropy.

If you need more confirmation that the "active player" is the one whose turn it is, not the one who is controlling the effect in question, see the timing structure, particularly phase 5.