The first is incorrect. All effects of a power with a keyword are considered to have that keyword. All effects of a power with Psychic and Fear are considered Psychic and Fear effects. Damage doesn't have keywords, it has damage types.
Damage types are not the same thing as keywords, even tho keywords often indicate damage types the power deals.
So let's say you have a power that deals fire damage, then poison damage, then scares them off. This power would have the Fire, Poison, and Fear keywords. Anything that keys off of or modifies powers with these keywords affects the entire power. Hellfire Blood, for example.
There are only a few instances where something has a keyword that the entire power itself does not have. These instances are when a power explicitly gives a keyword to a singular effect ("This effect has the fear keyword" on a power that does not have the Fear keyword) or when extra damage is assigned to a power that has a specific damage type (Burning Blade adds fire damage to what you deal, but does not make your powers Fire powers.) The general rule, however, is that all effects of a power share all that power's keywords, unless explicitly stated otherwise. (Try using Prismatic Ray with out that rule and Hellfire Blood--you can't, it does not work elegantly.)
So in the case of resistance/immunity it's pretty simple to understand. Resistance keys off of -damage types.- Immunity keys off of -keywords.- And keywords are in the header of the power, and apply to the whole power.