The video I did on inlays is a few years old and I'm doing it a bit different now. I really should update it but making videos really isn't my thing. Currently when I do an inlay I start with two pieces of wood about .4" thick, stack them and cut through. I'm using a #5 super sharp blade and set my saw about 1.6 degree angle. The angle depends on your blade size and brand, wood thickness and hardness. Sometimes my inlays end up a bit tight and then sometimes loose. After I glue the pieces in I run it through my drum sander to clean it up and end up with a finished piece that is about 3/8" thick.
When I did this tree the wood I used was 3/4" I set my saw at about 2 degrees because I didn't want the tree to push up as far as 3/8".
Hope that makes some sense to you. If not, send me a message and I am happy to share my phone number with you.