The #1 rule for DPSing for mages is to always be casting.
The #2 rule for DPSing for mages is to never stop mid-cast to do a different cast.
On the most basic level for TTW/Fire, DPSing follows the priority order of Living Bomb->Pyroblast->Fireball. However, it is really more complicated than that.
There are three main factors, in no order of importance.
1. Wasting as few Hot Streaks as possible.
2. Keeping up Living Bomb uptime as high as possible.
3. Keeping up 2T10 Bonus as high as possible, in the sense of having it apply to as many spells as possible.
So in the following scenarios, the order of importance will change depending on those factors.
For example, if back to back Hot Streak procs occurs, a mage would not use Hot Streak consecutively. The mage would do-
Hot Streak- Fireball-Hot Streak, or-
Hot Streak-Fireball-Fireball-Hot Streak, or-
Hot Streak-Fireball-Fireball-Fireball-Hot Streak.
This is to allow for higher uptime for 2T10 bonus, because Hot streak will simply reset the 2T10 bonus to 5 seconds. Choosing any of the three Hot Streak Scenarios depends on the last Fireball or Living Bomb critically striking and how close Living Bomb is to exploding.
In general, it is very much preferred to do Living Bomb before Pyroblast. This is because of two reasons-
1. Increased Living Bomb uptime.
2. To avoid wasting a GCD of time of 2T10, which would occur if Pyroblast-Living Bomb was done.
3. To reduce Ignite Munching.
To avoid this happening, pay attention to how much time left Living Bomb has before exploding. If Living Bomb is going to explode within 1-3 seconds, it would be wise to consider holding off using Hot Streak until Living Bomb explodes, then using Living Bomb then Hot Streak. Do not wait too long however, and pay attention to if the last few spells are critical hitting, because avoiding wasting Hot Streaks is desirable.
Remember that Living Bomb is not worth using if the enemy dies before the explosion, so if the boss will die before Living Bomb explodes, do not use Living Bomb even though this will lower Living Bomb uptime.