Hi
Can I ask how you add the second account ? Do you use just one mail account, and inside it click to add another mailbox ?
I ask as if you add two mail's profile, each of them need to have a license in order to work as Office 365 validate that the user can use the product. You could downgrade your Office license in worst case scenario, and buy the licensing to cover all the users inside the terminal server, but you will loose maybe in the end as you already have Office 365's user covered to use the current product. Better scenario would be to cover everyone to use Office 365