You have to learn that the more aggressive the bit...the more dangerous it is to you and your tree (though they are ALL DANGEROUS). I will categorize the terrier, weasel, & router bit at the most dangerous. Burrs like you showed, is slower but accidental mistakes cannot cause much damage as fast.
As with any rotary tools, avoid anything dangling, wires, thread, hair, laces, etc. It is debatable but some believe it is safer to not use any gloves when using rotary tools. If you do, use an all leather gloves...something that will cut and not get pulled (like thread).
Eye protection is a must...those chips (projectiles) fly at an awfully fast phase!
Experiment with a plain wood/branch (secured on a vise or nailed somewhere stable). Feel how the bit behaves with light touch vs aggressive cut. See what happens when it "catches" on something and how much force it will pull you. Do this before you touch a tree...else you may lose a very important branch in an instant.
Also note that green wood (fresh) cuts very differently compared to dry wood.
Good luck and be safe!