The doubly-fed induction generator (DFIG) is considered to provide a low-reactance path in the negative-sequence system and naturally comply with requirements on the negative-sequence reactive current in emerging grid codes. This paper shows otherwise and how the control strategy of converters plays a key role in the formation of the active and reactive current components. After investigating the existing control strategies from the perspective of grid code compliance and showing how they fail in addressing emerging requirements on the negative-sequence reactive current, we propose a new coordinated control strategy that complies with reactive current requirements in grid codes in the positive- and negative-sequence systems. The proposed method fully takes advantage of the current and voltage capacities of both the rotor-side converter (RSC) and grid-side converter (GSC), which enables the grid code compliance of the DFIG under unbalanced three-phase voltages due to asymmetrical faults. The mathematical investigations and proposed strategy are validated with detailed simulation models using the Electric Power Research Institute (EPRI) benchmark system. The derived mathematical expressions provide analytical clarifications on the response of the DFIG in the negative-sequence system from the grid perspective.