What is the timing of a Rod of Absorption’s spell-absorbing reaction?

Suppose I have a Rod of Absorption, which has this ability:

While holding this rod, you can use your reaction to absorb a spell that is targeting only you and not with an area of effect. The absorbed spell’s effect is canceled, and the spell’s energy — not the spell itself — is stored in the rod. The energy has the same level as the spell when it was cast. The rod can absorb and store up to 50 levels of energy over the course of its existence. Once the rod absorbs 50 levels of energy, it can’t absorb more. If you are targeted by a spell that the rod can’t store, the rod has no effect on that spell.

If an enemy is casting a spell at me, when do I decide whether to use my reaction to absorb it, and how much information do I have about the spell being cast at me at the time I make that decision? For example, the enemy who is "casting a spell at me" might be targeting me with the area of effect of a Fireball, or targeting me with Charm Person, or targeting me and 2 other people with a 3rd level Charm Person. Only one of these cases satisfies the conditions for absorbing the enemy spell, so it seems that I need to know what spell is being cast and who it is targeting before I can even decide if it is possible for me to use my reaction to absorb it. However, it doesn’t necessarily make sense for me to have this information at the time the spell is cast. An alternative interpretation could be that when a spell is cast, I use my reaction to attempt to absorb it, but if the spell cannot be absorbed then my reaction is wasted with no effect. This seems like an unsatisfying interpretation, especially in a situation where multiple enemies are casting spells and wasting my reaction on a spell that I can’t absorb leaves me open to another spell that I could have absorbed. On the other hand, the last sentence of the quoted paragraph seems to lend some support to this interpretation, although it’s possible that sentence is only referring to the rod’s limited storage capacity.

So, is there an interpretation that best fits with RAW, or is all of this in the territory of DM ruling?

Note: You may assume that we are playing with the optional rule from XGtE for identifying a spell. In practice, this will mean that I cannot use my reaction to identify the incoming spell, because then I won’t have a reaction available to use with the rod. Additionally, as the example above shows, even knowing the identity of the spell being cast doesn’t guarantee that I will know whether it can be absorbed.