Following the COVID-19 pandemic, many countries worldwide have put lockdowns in place to prevent the virus from spreading. Evidence shows that lockdown measures can affect mental health; it is, therefore, important to identify the psychological characteristics making individuals more vulnerable. The present study aimed, first, to identify, through a cluster analysis, the psychological attributes that characterize individuals with similar psychological responses to the COVID-19 home confinement; second, to investigate whether different psychological characteristics, such as personality traits, alexithymia, and resilience, specifically influence anxiety, stress, and depression, depending on the scope of the confinement. We analyzed data from 393 participants who completed an online survey on their experiences during two different phases of the Italian lockdown, characterized by more or less strict measures of confinement. Two clusters were identified which included participants reporting a better (+ER) and worse (-ER) emotional response to the lockdown, respectively. Individuals in the -ER group showed lower emotional stability, resilience, and higher alexithymia. Moreover, even if lifting part of the restrictions decreased psychological distress among all participants, a reduction in perceived stress was observed only among individuals with high resilience. Finally, personality traits, alexithymia, and resilience differently affected depression, anxiety, and stress. Our results suggest that different psychological interventions should be planned depending on the context: mental health professionals should focus on enhancing the individuals' coping strategies to alleviate stress in emergencies, while long-term intervention aiming at alleviating anxiety and depressive symptoms should focus on alexithymic tendencies and personality constructs.