Q. Do I need to cite all original sources for AMA?

In-text, you would need to cite any source that you quote directly, or any information or idea that you paraphrase.

In your reference list you should only cite materials that you have read.

You do not cite the sources the author of an article you read uses, unless you have read them yourself.

AMA does allow for the citing of secondary sources, i.e., say, citing a quote in the article you read that the author is quoting from another work. Please see pp. 61-62 of the AMA Manual of Style, 10th edition, for examples.