When are targets chosen in Final Fantasy TCG?
This was explained in a tweet from the developer:

Question
「選ぶ」ある召喚獣やアビリティがあります。使う時に選ぶと思うが11.11.4.1.1.以外「選ぶ」を特別扱うルールは見つけることができないので結果の一部として解決時に選ぶべきも思われます。どっちが正しいですか。ルールにその答えがいたならその番号も教えてください。
There is a summon and abilities that &quot;choose&quot;. Although 11.11.4.1.1. Other than &quot;choose&quot; a special treat rules also seems to choose at the time of resolution as part of the result because it can not find think that choosing when to use. Which is correct? Please also tell me the number if the answer was in the rules. (Auto-translated through Google Translate)
Answer
選ぶのはアビリティを使用する際になります。総合ルールに明記されていませんので、次の更新の際に追記いたします。ご指摘ありがとうございます。
It will be when you use the ability to choose. Because not explicitly stated in the Comprehensive Rules, it will be appended to the time of the next update. Thank you for your advice. (Auto-translated through Google Translate)

In other words, targets are chosen when the card is used. It has not been added to the comprehensive rules by mistake.