Records indicate that 14,500 years ago, sea level rose by 12‐22 m in under 340 years. However, the source of the sea level rise remains contentious, partly due to the competing climatic impact of different hemispheric contributions. Antarctic meltwater could indirectly strengthen the Atlantic Meridional Overturning Circulation (AMOC), causing northern warming, whereas Northern Hemisphere ice‐sheet meltwater has the opposite effect. This story has recently become more intriguing, due to increasing evidence for sea level contributions from both hemispheres. Using a coupled climate model with freshwater forcing, we demonstrate that the climatic influence of southern‐sourced meltwater is overridden by northern sources even when the Antarctic flux is double the North American contribution. This is because the Southern Ocean is quickly re‐salinized by Antarctic Circumpolar water. These results imply that the pattern of surface climate changes caused by ice sheet melting cannot be used to fingerprint the hemispheric source of the meltwater.