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This study examines the asymmetry in the Indian summer monsoon rainfall (ISMR) response over India and its four homogeneous regions to two distinct types of temporal evolution in La Niña. We have shown this uneven response by analysing the large‐scale dynamics over tropical Indo‐Pacific region for the period 1951–2022. We have identified two types of La Niña events during monsoon season (June–September) based on whether they evolved from El Niño or La Niña from preceding boreal winter season (December–February). India receives significantly more (less) rainfall during La Niña years, when it was preceded by El Niño (La Niña) in the preceding winter. We further observed the spatial diversity of rainfall over India with a northeast–southwest dipole pattern. When La Niña years were preceded by El Niño, positive surface pressure anomaly over west‐north Pacific, low‐level westerlies and moisture transport favoured the rainfall over south peninsula and west‐central India. Whereas moisture divergence associated with anomalous lower‐tropospheric anticyclone over west‐north Pacific suppressed the rainfall over Indo‐Gangetic plains. However, when La Niña years were preceded by La Niña in winter, the absence of westerlies and weak moisture transport subdued the rainfall over south peninsula and west‐central India. At the same time, moisture convergence and a greater number of monsoon depressions favoured rainfall over north‐west India. This study also looked at how well eight Copernicus Climate Change Service (C3S) models predicted ISMR and SST for two types of La Niña with April initial conditions during the period 1993–2016. Models were able to capture the spatial pattern of SST anomalies over Indo‐Pacific Ocean, but all models could not capture the spatial pattern of ISMR. However, in terms of intensity, six out of eight models could predict more (less) ISMR when it was preceded by El Niño (La Niña), coinciding with the observed anomaly. [ABSTRACT FROM AUTHOR]