This study examines the role of cross-linguistic transfer versus general processing strategy in two groups of heritage speakers (n = 28 per group) with the same heritage language -- Russian -- and typologically different dominant languages: English and Estonian. A group of homeland Russian speakers (n = 36) is tested to provide baseline comparison. Within the framework of the Competition model (MacWhinney, 2012), cross-linguistic transfer is defined as reliance on the processing cue prevalent in the heritage speaker's dominant language (e.g. word order in English) for comprehension of heritage language. In accordance with the Isomorphic Mapping Hypothesis (O'Grady and Lee, 2005), the general processing strategy is defined in terms of isomorphism as a linear alignment between the order of the sentence constituents and the temporal sequence of events. Participants were asked to match pictures on the computer screen with auditorily presented sentences. Sentences included locative or instrumental constructions, in which two cues -- word order (basic vs. inverted) and isomorphism mapping (isomorphic vs. nonisomorphic) -- were fully crossed. The results revealed that: (1) Russian native speakers are sensitive to isomorphism in sentence processing; (2) English-dominant heritage speakers experience dominant language transfer, as evidenced by their reliance primarily on the word order cue; and (3) Estonian-dominant heritage speakers do not show significant effects of isomorphism or word order but experience significant processing costs in all conditions.