In many missions, the commentary from the crew on the Argo triggers out of sequence with the events in the mission. For example:

Base assault, supposed to be abandoned. As I approach turrets appear on sensors. Move in to range, destroy 2 turrets. Top of next round, Darius announces that reinforcements are inbound. I advance towards base to get remaining turrets, and Sumire pops up to comment that the "abandoned" base has live turrets. Duh, I've already killed 2. Destroy the remaining turrets, and with no further comment a lance of mechs drops right outside the base.

To me, it seems that Sumire's comments about turrets should have triggered as soon the first one appeared on my sensors, and Darius' warning about inbound reinforcements should have triggered when I destroyed the third turret (of four.) Is this a common problem, and can I fix it?

That's what it looks like to me as well, seems like events could trigger on a sensor target, or a dropship actually landing, rather than just on a map point.