The Atlantic SST dipole index, reflecting the interhemispheric seesaw response of sea surface temperatures to variations in the Atlantic meridional overturning circulation (AMOC), has been proposed to approximate AMOC variations over the duration of the instrumental temperature record. Using historical and control simulations of the CMIP5 dataset, here we investigate whether this index provides a good proxy for the AMOC variability on decadal to centennial timescales and whether in fact the SST response on these timescales is interhemispheric in nature or centered more on the North Atlantic. We find that the power spectra of AMOC variations and the Dipole index share common spectral peaks in many models, and the two indices typically correlate with coefficients between 0.2 and 0.8 with a few year lead. However, the multi-model ensemble average is only 0.5, explaining about a quarter of the AMOC variance. Furthermore, we find that even for the models with the highest correspondence between the AMOC and the Atlantic dipole, the correlation between the two is controlled mainly by SST variations in the North Atlantic. Taking into consideration the South Atlantic SSTs does not improve this correlation, and in many cases makes it even worse. We conclude that on decadal to centennial timescales AMOC variations mainly affects the North Atlantic, with an SST sensitivity of about 0.3oC per 1Sv given by the CMIP5 multi-model average. At the same time, a significant fraction of climate variability in the Atlantic appears to be unrelated to AMOC variations.