In the verse, “Take ye therefore good heed unto yourselves,” the care refers primarily to the spiritual soul. However, one cares for the corporeal soul even without commandments from the Torah. This is because the rule is that a Mitzva is primarily evident, meaning it is evident that he does what he does for the purpose of a Mitzva when he would not do it, were it not for a Mitzva. Rather, the reason he does it is because of a Mitzva.
Hence, with a Mitzva that he performs, if he would do it even if it were not a Mitzva, he needs special care, to find a place where he can say that he does this only because of a Mitzva. Then the Light of the Mitzva can shine on the act of the Mitzva that he performs. This is called “making a Kli with the Mitzva,” in which the Upper Light can be. Hence, the care refers primarily to the spiritual soul.