Note that OP mentioned an HSA -- with that type of account (goes along with a High Deductible health plan) you don't send receipts in; the bank doesn't get involved in authorizing expenditures; they simply report the total to the IRS at the end of the year, and you keep your records to justify if the IRS audits you.

You have a lot of flexibility -- you can pay expenses directly from the account, reimburse yourself right away by writing a check to yourself, reimburse yourself at the end of the year, or even years later. There are tax and other strategies behind each.

There's no reason not to pay expenses with a personal card -- it can actually simplify things if there are any adjustments later (I had our dentist refund $8 with a check to me after I'd paid with the HSA debit card; luckily we had some eligible expenses not paid from the account so I didn't have to find out how to send in a "refund" that's not a deposit).

With my HSA, the only way I know of to get reimbursement is to write a check to myself (there may be other ways to do it); they sent a checkbook when the account was opened. The "Do That" consists of keeping good records and making sure the expenses match what the HSA bank reports as the distribution (I have a spreadsheet matching with the filed statements).

Some of this may apply to other medical accounts where you do send in receipts; YMMV.