Do we make predictions in our time, or local time?
We express when events are going to happen (or have happened) in our observed time frame. 

For example, we say SN 185 went supernova in the year AD 185; but it didn't. The star actually physically exploded about 9,100 years earlier. 

When we say the sun will set tonight at 8:07 PM ET, that is when we observe the event. But our actual position relative to the tangent from the sun will have already passed about 8 minutes 20 seconds earlier (plus several minutes due to atmospheric refraction).

So when you say Betelgeuse is predicted to explode sometime in the next million years, that's how many more Earth years are expected to pass until we see it happen&hellip; from here. From Betelgeuse's point of view, it would have happened about 642 years earlier&hellip; or it may have happened already.