With the sample provided, there's no clear right or wrong answer to your question, other than to say that, as stated, the student's sentence is unclear.
Part of the problem is the use of the word when.
"She was astonished when she opened her gift because it was always what she wanted."
This wording implies to the reader that she has only opened one gift, and this is when she did it. However, it was always implies that in reality, this one of of many times she has opened a gift, and consistently when she opened the gift, it was something she wanted.
Ideally, this circumstance is when English uses the word whenever.
"She was astonished whenever she opened her gift because it was always what she wanted."
Stated this way, it describes a story with repeating incidents.
And finally, the last problem with this sentence, what she wanted, swings us back to hearing it possibly the other way. Usually, a native English speaker would say "something" rather than "what", if the idea was to describe a repeating scene.
So, in summary, you could be right (and probably are), in that the student was really trying to say, "She was astonished when she opened her gift because it was what she always wanted." But when you're dealing with someone for whom English is not native, sometimes you have to parse the sentence more than at first blush seems reasonable.