Using HSA card to pay medical bills, then submitting to BCBS for deductible credit + reimbursement — tax implications?

I have a High Deductible Health Plan with Blue Cross Blue Shield and an HSA. A family member gets covered medical treatment. I pay the provider's monthly bill directly with my HSA debit card. Then I submit the claims to BCBS so the expenses count toward our annual deductible.

Once the deductible is met, BCBS (in theory) reimburses me for the amounts I already paid with HSA funds.

Previously, I paid these bills out of my checking account, submitted claims, and got reimbursed by insurance once the deductible was hit. The only difference now is using pre-tax HSA money instead of post-tax bank money.

Question: How does this work from a tax perspective? Is there anything I need to watch out for? It feels like I might be missing a step or creating a tax issue.

Any experiences with this setup (especially with BCBS)?