Yes, you are correct. Invisibility can only be played to evade a monster you encounter. If you make the text explicit, the wording would be:
"You discard this card to allow you to evade a monster."
That makes it clear how it works, but is more clunky to read and say.
No One Else Can Take Your Turn for You. Whenever you encounter a card or make a check, you—and only you—must resolve it. No other character can evade it, defeat it, acquire it, close it, decide what to do with it, or fail at doing any of those things. If the game tells you to do something, you have to do it.
That being said, notice the difference between Sanctuary and Invisibility. Sanctuary can let someone else evade something, but because the action you perform with Sanctuary is choosing a character, and that character does the evading.
What makes Invisibility unique is that it lacks the Mental trait, which you will find on most spells that allow you to evade something. And it really comes into its own if Ezren is in your group and takes the Illusionist role.
In Wrath, cards like this will say something like "Discard this card to evade a monster you encounter."
I know you don't technically need to do that for the rules to work, but I'm glad to see this change, as it makes explaining the rules so much easier.