Yes, it would take loading 4-5 splits on that starter fire to warm things up. Then it should be at temp in about 20-30 mins.It'll probably take a long time with a fire that small...
The current outside temps are working against you, especially if the chimney is short and more so if the liner didn't get insulated. When you start up the insert at 45F or below it will start behaving quite differently and there should be no smoke spillage. Here is a short video which has good tips for starting the fire. Watch the "Efficient Woodstove Operation" video.
http://woodheat.org/wood-heat-videos.html