Yes it does, Umero. The cast time is halved, but the global is still a full 2.5 seconds. That makes it so it's 18 seconds before the next cast is available. However, it's also worth noting the potency numbers are far far off.

AF is a 40/60/80% potency increase for fire, UI is a 10/20/30% potency penalty. So, if you get both procs...

Flare > Transpose > Thundercloud > Firestarter
4s s + 0.5s + 2.5s + 2.5s = 9.5 seconds before rotation can continue (will not be at max MP)

468p + 0 + 340p + 198p = 1006 potency
105.9 p/s

Flare > Firestarter > Transpose > Thundercloud > B3 > B1/Scathe > Fire 3
4s + 2.5s + .5s + 2.5s + 3.5s + 2.5s + 2.5s = 18 seconds before rotation can continue (should be at max MP)

468 + 396 + 0 + 340 + 220 + 150/100 + 154 = 1728/1678 potency
96 (93.2) p/s.

But, considering that you'd likely only be able to get one fire off using the first rotation before going back into Umbral Phase, it's more likely for it to deal less overall damage.