It is possible to receive the second and third hints before the first hint if one does not finish the initial dialog.

How does that work, exactly?

Hints are on a timer and automatically pop up, regardless of location, what you're doing...etc.

Does the "1 minute deadline" start when you hit Mission Start, or does it run from the timer?

2 days in, about 6 runs done and I believe you get some leeway for reading the dialogue box.

I started 6:30 min in, I finished in about a min, I got 3 AP. I believe the timer starts at the beginning of the mission, someone else also test this please.