This could be related to the job role defined for the employee which might need some changes.
To start with, please refer to the below article on POS fresh setup: Aloha POS Punchh Integration (Fresh Install)
To be specific, look for the "Table Service - Check-in, Create a new order entry panel to allow for the 'Check In' button to be available". Please check if the Employee has the same job code as others (who are able to see the check in button)
Please reach out to Punchh Support if the issue persists.
If further assistance is required, submit a ticket to Punchh Support. (For help submitting a ticket, click here)