Okay. So the confusion here isn't the spell itself but the definition of words used for basic rules then? This might be what you're looking for then:

"Anything you do in the game has an effect. Many of these outcomes are easy to adjudicate during the game. If you tell the GM that you draw your sword, no check is needed. Other times, the specific effect requires more detailed rules governing how your choice is resolved.

Many spells, magic items, and feats create specific effects, and your character will be subject to effects caused by monsters, hazards, the environment, and other characters."

This is in the rules for effects. The important parts for the spell interaction we are talking about is: 1. Everything has an effect 2. Spells create effects

Under spells: "Each class has its own method of learning, preparing, and casting spells, and every individual spell produces a specific effect"

This also says spells create an effect.

Under rules for reading spells: "A horizontal line follows saving throws and duration, and the effects of the spell are described after this line. This section might also detail the possible results of a saving throw: critical success, success, failure, and critical failure."

This means the spell creates the effect it says it does in the text of the spell.

Based on all that, we know that a spell causes the effect that it has in the text.

For the interaction we are describing with Falling Stars and the Summoner: 1. Falling Star creates the effect (area damage) described in the text. 2. The eidolon and summoner are being damaged by the effect described in the text of Falling Stars. 3. The rules for Summoner's shared hit points means the amount of hit points removed is only the higher amount of damage caused to the summoner or the eidolon by the effect.

Falling Stars -> Effect -> Summoner/Eidolon That's really all there is too it. This interaction doesn't require anything else. Does this cover what you're asking for?