She got jealous whenever he talked to other girls.
Literal
She [topic-は] he [subject-が] other girl [to-に] [calls-out-to-話し掛ける] [whenever-と] became-jealous.
話し掛ける is a compound verb: 話す ('speak') + 掛ける, where ~掛ける lends the sense of 'doing toward / initiating action toward.' It takes に for the addressee. The conditional ~と signals habitual, near-automatic consequence.