Ice, it does proc from dots. Ignite procs from any fire damage crit, including DoTs. This is actually a BAD thing though, because your fireball and pyroblast crits can get munched by all those dots that are popping and refreshing ignite.

If you don't believe me, I went to WoL and picked a random mage in the top 200 of the Argolath encounter. The first damage that shows up is a living bomb DoT tick (not the explosion, but the tick), that crit for 11426. Before his next crit, an Ignite tick shows up for 2913 (it's higher than the expected 20% which would be 2285 because of mastery, which does affect ignite).

Now, I'm hoping this doesn't get overly mathy for everyone, but look at this sequence right here, which shows ignite munching I think to a T:

[23:56:50.029] Tirsten Combustion Argaloth *16084*
[23:56:50.284] Tirsten Living Bomb Argaloth *8476*
[23:56:50.629] Tirsten begins to cast Fireball
[23:56:50.844] Tirsten Combustion Argaloth 8062
[23:56:51.661] Tirsten Fireball Argaloth 14972
[23:56:51.661] Tirsten Combustion Argaloth *16084*
[23:56:52.573] Tirsten Pyroblast! Argaloth 1547
[23:56:52.597] Tirsten Combustion Argaloth *16084*
[23:56:52.785] Tirsten begins to cast Fireball
[23:56:52.785] Tirsten Living Bomb Argaloth *8476*
[23:56:53.045] Tirsten Ignite Argaloth 2162 ------------------- Ignite
[23:56:53.362] Tirsten Combustion Argaloth 8062
[23:56:53.669] Tirsten Fireball Argaloth *29577*
[23:56:54.234] Tirsten Combustion Argaloth *16084*
[23:56:55.013] Tirsten begins to cast Fireball
[23:56:55.013] Tirsten Pyroblast! Argaloth *3085*
[23:56:55.013] Tirsten Combustion Argaloth *16084*
[23:56:55.044] Tirsten Ignite Argaloth 2161 -------------------- Ignite

In a span of 5 seconds, we have 9 separate critical strike hits. But as you can see, the damage of Ignite is the same (2161 and 2162 can be considered the same from rounding up and down). The next ignite tick in this log is this:

[23:56:57.044] Tirsten Ignite Argaloth 1965

Which means that all of the combustion plus that 30k fireball crit got munched, likely by that pyroblast dot crit you see for 3085. Had the fireball crit been added instead, that next ignite tick would have been closer to 6000, not the 1965 that showed up. And had ALL of those crits been added, we would have seen closer to 18,000 damage per ignite tick added.

Because of munching, this guy lost a total of 52k ignite damage (before mastery) in this sequence.

These numbers are reproducible, and you can look at any mage's log on a single target encounter and find the same phenomenon.

If you understand what I'm saying, you are probably as sick to your stomach as I was when I looked at how much damage is being lost by ignite munching.