"Under Income the contribution amount is stated under Box 12 "W" and then TurboTax asked me to enter in my 1099-SA HSA contributions as well, designating also that it is tied to a HDHP. It positively affected my refund in that case. Is this an accurate procedure?"
Yes, when you entered your W2, the box 12 W amount was added as income thereby increasing your taxable amount (lower refund). After you had acknowledged HDHP insurance, the amount was removed from income and your refund increased. This is a common source of confusion and question about how and why the program behaves this way.
