Really not difficult to see it's like a normal pattern for kata but with a bit magic pen
Which help in mid and late game because there are only three item that give magic penetration.

This probably one of the crazy choice for other player but i think deathfire is better than thunderlord.
Pros of Thunderlord:
-Just a very good start with a lot of damage
-This masteries is for a little trade which deal a lot of damage
Cons of Thunderlord:
-This masteries have a cooldown not very short (15 sec) so in the early mid game this became worst than Deathfire touch
-Not very good for long trades and for make a lot of damage in late/mid
-You don t have a lot of magic penetration without Piercing Thoughts


Pros of Deathfiretouch:
-Deal a lot of damage with just Q or E of kata
-She is like a little ignite so this could help you to kill more easily people with shield
-You have 7% of magic penetration
Cons of Deathfiretouch:
-Need of a buy for become better of Thunderlord
-Not good for burst damage

Here there is a link for the League of Legend Wiki where they explain the difference beetwen this masteries : leagueoflegends.wikia.com/wiki/Deathfire_Touch_(Season_2016_Mastery)
[EDIT] Since the nerf of kata early game i will advice is better play safe until level 6

Start from red and jump on the wolves, after take blue buff and gromp. If you don t have hp for clear jungle just kill the little mob in the river (just need some practice)
Ganking with shunpo and reset is preatty easy (like when you roam bot)

EDIT(01/04/17)
With the reowork of the masteries my masteries pages is good only with the tank (high magic resistance)
Because now precision is more efficient with squishy target
You can found this in the wiki ^^

My stats with katarina
My last game
Alexbuttafuori, is summoner name you can see my stats with kata