They placed under him

He offered because he would come in his place (in the source: He placed it as a cushion under him to improve the comfort of sitting. Under the meaning of a bed from..., or: in place, a place).

("As for the sabbaths, in clothing and in the offering of the sabbath, it is forbidden, in the offering of the sabbath - and he said (and read 19) it shall not come upon you - but you are permitted to offer it under you, but the sages said: It is forbidden to do so, for what you have bought is only one upon his flesh" - Yoma Seth 6:1, and so: "From the sabbaths, and according to this, in the tallit of Shaula, it was forbidden to offer it under him And who would see that there is a distinction between a tallit, the whole purpose of which is to wear it for the sake of one's own pleasure, and priestly garments?" - Tossofot Masekhet Chulin Ki b)

Translation