No you are not suppose to pay GST under RCM as supply is from a registered person and this is only a reimbursement.
As per section 7 of CGST Act read with schedule III of CGST act:
Services by an employee to the employer in the course of or in relation to his employment is not treated as a supply, so there is no question of charging GST.
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chatCommentsThanks - Ashok Modi