Understanding the interaction between the tropical Pacific and Atlantic Oceans has challenged the climate community for decades. Typically, boreal summer Atlantic Nino events are followed by vigorous Pacific events of opposite sign around two seasons later. However, incorporating the equatorial Atlantic information to variabilities internal to the Pacific lends no significant additional predictive skill for the subsequent El Nino-Southern Oscillation (ENSO). Here we resolve this conundrum in a physically consistent frame, in which the nascent onset of a Pacific event rapidly induces an opposite-signed summer equatorial Atlantic event and the lead correlation of Atlantic over Pacific is a statistical artifact of ENSO's autocorrelation. This Pacific-to-Atlantic impact is limited to a short window around late spring due to seasonally-amplified Atlantic atmosphere-ocean coupling. This new frame reconciles the discrepancies between the observed and multi-model simulated inter-basin relationship, providing a major advance in understanding seasonally-modulated inter-basin climate connections as well as their predictability.