No, it does not matter if the contribution comes from an employer contribution or out-of-pocket. You can maximize the contribution limit if you are both over the age of 55 by each spouse having their own HSA. Then, your contribution limit for the family becomes $9,200. As long as at least $1,000 is deposited into each HSA, the remainder of the contribution as well as whether it was an employer contribution or out-of-pocket does not matter for tax purposes.
@Big0taxes
