I bet I can give the method they use to discern the two.
Many believers assume as a matter of course that their God loves what they love, supports what they support, and hates what they hate.
So it stands to (their) reason that whenever something bad happens to their enemies, it must be happening to God's enemies as well, and therefore, it's God's punishment. OTOH, if it happens to someone whom they have no reason to hate, then
most of the time it will be written off as a "natural disaster."
I say "most of the time," because there are some believers who continually believe that they are underestimating God's ability to hate, and will assume that the people being hit have committed some offense for which they have deserved obliteration.
Funny, isn't it? Believers (around here and elsewhere) are quick to believe that God hates more than they do; not so quick to believe that He loves more than they do.