I just recently had to use insecticidal soap on a Rhododendron and if I recall well the label did mention testing it on a small area to see if a particular cultivar to be sprayed is sensitive to it. So I guess there is a chance your Azalea might be susceptible to damage from such product. Maybe try washing it off?

Ok I was gonna water it with the oscillating sprinkler tomorrow anyway. Also the label on mine did not have any precautionary statements about that.

Also, do you know if my azalea will ultimately die from this?

If there are yellowing leaves in only a few places, it could be entirely coincidental. Evergreen azalea leaves naturally turn yellow before dropping and being replaced by new leaves. Acute sensitivity in one variety is possible, but very, very unlikely to be seriously damaging, let alone fatal. Testing on a small area first is good practice no matter what sort of spray is used. Equally important is not spraying in bright, hot, direct sun.

Or when temps are 85 or higher.