Your sentence is not conditional, there is no hidden "if" anywhere. It is true that sometimes when can be used instead of if, but here you have whenever which means every/each time. This sentence speaks of a habitual situation in the past which started at a past moment marked by ever since. Therefore,
Ever since she got her test results back,
does not speak of a condition, but tells you when that past frequency started. The repeated action in the past is marked by would in the main clause
she'd [would] get mad
As for the rest of the sentence
whenever someone asked her about it.
shows you when or how often that action is repeated. What may have confused you is that the main clause has two time modifiers, one showing when the past situation started and another saying how often the action is repeated. Though the structure of the sentence may seem somewhat particular, it is nevertheless correct to mark different aspects of the past time with two time clauses.