Does it mean I'm paying for medical expenses two times?

In a way, yes - however it is temporary.

1. First, you pay for the medical expense personally out of your pocket.
2. Then, your corporation pays the same amount to your health spending account provider to process the claim for this expense.
3. Once the claim is processed, your health spending account provider then reimburses you (personally) fully.

So, while it seems like you pay twice, your corporation benefits from a tax deduction and you are reimbursed (personally) tax-free.