It is widely accepted that the signature of anticyclonic (cyclonic) eddies on the sea surface temperature corresponds to a warm (cold) core anomaly. Nevertheless, this statement has been put to question by recent regional studies showing the existence of inverse eddy SST anomalies: cold-core anticyclones and respectively warm-core cyclones. This study shows that the emergence of these inverse signatures is a seasonal phenomenon that affects the life cycle of mesoscale eddies in the Mediterranean Sea. We use remote-sensing observations and in-situ data to analyse the eddy-induced SST anomaly over a 2 years period (2016-2018). We build an eddy core surface temperature index to quantify the amount of Cold Core Anticyclones and Warm Core Cyclones all over the year and especially during the spring re-stratification period. We find that these inverse eddy signatures could reach a peak of 70 % in May and June, both for cyclones and anticyclones. Besides, in order to understand the underlying dynamical processes, we construct a simple vertical column model to study the impact of the seasonal air-sea fluxes on the surface stratification inside and outside eddies. It is only by taking into account a differential diapycnal eddy mixing - increased in anticyclones and reduced in cyclones - that we reproduce correctly, in agreement with the observations, the surface temperature inversion in the eddy core. This simplified model, suggests that vertical mixing modulation by mesoscale eddies might be the key mechanism that leads to the eddy-SSTA seasonal inversion in the ocean.