Infusion question

In the ED facility setting, please clarify what is considered a subsequent infusion vs. an additional initial infusion.
Would the Dilaudid be coded to a subsequent infusion (96367) or as another initial 96365-59 because it is given at a different site?

Example:
Infusion of Zosyn given in RT antecubital 0735-1113
Infusion of Dilaudid given in LT hand 0643-0730

THANKS.