I am not familiar with your type of tipi, but general precuations for fire are to keep the area around the fire bed clear of combustibles. At least 18 inches separation is needed for a small cooking fire, double that for a larger "warming" fire.
Allow adequate overhead clearance to ensure nothing is flammable for 6 ft. above a small fire, 10 ft. or a clear opening to sky twice the diameter of the fire is better, especially if you have occasional rising sparks.
While the fire must be protected from wind, be extremely cautious about carbon monoxide when sheltering. Keep a fire bucket of dirt, sand or water handy to extinguish the fire if you have any unintended flare-ups or extension of the fire.
Best is to build a small fire in a container such as a coffee can heater. This can be readily picked up and moved outside, or smothered by covering. Putting your small cooking fire in a metal container also conserves limited fuel and radiates heat more effectively.
OK, this is somewhat misleading, since I have NO IDEA how your 'Tipi' is made...
The actual TRADITIONAL Native American Tipi is made from animal hides, so the leather on top is already fire resistant.
The design of a properly and authentic Tipi will have a liner in the bottom of the Tipi, then the outer shell that give it the distinctive shape.
Air flow from outside comes in between the liner and the upper and helps keep the heat from the fire from overheating what ever material the upper is made from.
The height of the Tipi also helps keep the fire from overheating the lodge poles or Upper material.
The liner will have a hole in the middle for a small 'Fire Circle', and the smoke exit hole at the top will be a flap that can be closed or restricted during bad or cold weather.
Most people don't know it, but the liner really is the 'Secret' of how such a 'Primitive' shelter can be so successful at keeping one warm and dry!
For a 'Modern' Tipi, I'd keep to a smaller 'Hobo' or 'Rocket Mass' type heater that was more efficient at extracting and radiating heat from the fuel you use.
Early Tipis and their lodge poles were often treated with Borax to keep bug infestations from happening and for a fire retardant.
Today, you can use a solution of Boric Acid for the same reasons.
The smoke that permeated everything in the Tipi worked as a natural insect repellant, and Boric Acid solution allowed to soak into the material will act as insect repellant/killer, and it's also a fire retardant...
A VERY good thing since you will probably be using something that is more flammable than buffalo hide for your Upper shell!