One could constitute Aschenbach's death as both self-inflicted and uncontrollable.
One could justify that Aschenbach's death was self-inflicted. Given that he makes the choice to stay in the cholera-ridden Venice, one could state that the consequence of staying in Venice (because of his sexual infatuation for Tadzio) led to his death (his getting cholera). Therefore, if he would have left Venice, Aschenbach would not have gotten cholera and he would have lived.
On the other hand, a person cannot control who they have feelings for. Therefore, Aschenbach gets cholera as a result of the outbreak and his inability to leave the place where Tadzio is. Since he cannot control his heart, Aschenbach cannot control his death. As obsessed as he is with Tadzio, leaving Venice may have "killed" him as well.