Welcome.
Be patient. There is wide variability in how long this process takes; and how smoothly it goes. We don't know why. My buyout was seamless; involved one phone call to KMF, and c. a month later I had the title in my hands. I do know that it isn't KMF that does the buyout; it's HCA Exchange, Inc. That's who I made out my personal cheque to.
One week isn't a done deal on updating your KMF account page. During the process, I'd checked back on my buyout page and as the day for my next monthly lease payment drew nearer, my page still did not show that anything was in the works. Be confident, that if you make another lease payment, that it will come off the amount of the buyout. Kia isn't going to stiff you for a payment made while the buyout was progressing.