Which tense to use depends on your meaning, i.e. what information you want to express.
In the simple case, when Amy is currently a student, then John is correct.
But, if Amy was a student who left school, then past tense is possible. e.g. Amy is now a university student, and her high school teacher is talking about her, then 'Students such as Amy liked reading books'.
It's even possible that if Amy is a student in a school in a poor country, and someone has just built a library, that she will be soon able to use, then 'Students such as Amy will like reading books'.
There are even more complicated possibilities with more complicated tenses.