advance money, pay for another
墊 centers on covering a cost on someone else's behalf: advancing money or paying for another person.
墊 combines 執 (hold, take charge) with 土 (earth, ground), suggesting the idea of putting something down or covering a cost. The exact historical development is uncertain.
The top 執 looks like someone holding something, and the bottom 土 is the ground. Imagine a person holding money and placing it on the ground to cover a payment for someone else.
For テン, picture ten (テン) coins being advanced to a friend: ten -> テン, and you pay for them.