We have a swordmage Genasi running Extra Manifestation and Elemental Tempest. Most of the time she's in fire Genasi form. When she uses an action point, she gains resistance to the damage type of her choice by manifesting another Genasi manifestation. So far I've seen her running cold resistance, thunder resistance and necrotic resistance. Is that allowed by the rules or are we doing something wrong?
An Elemental Tempest can choose any standard manifestation when they use an action point.
From the FRPG, p53 (emphasis mine):
Elemental Surge: Whenever you spend an action point to take an extra action, you can choose to adopt any one of the five elemental manifestations. If you cannot normally manifest the element you choose, you gain the benefit of that manifestation until the end of the encounter. If you choose a manifestation that you can normally use but are not currently using as a Dual Manifestation (see above), you can immediately change which two manifestations you are using.
So an Elemental Tempest can choose any of the standard elemental manifestations (Earth, Fire, Storm, Water, Wind) when they use an action point. By RAW they cannot choose one of the corrupt manifestations (Caustic, Cinder, Plague, Void) or Athas manifestations (Ember, Magma, Sand, Sun), though it would be a pretty reasonable house rule to allow those as options.
It's important to note that this ability lets the character choose a manifestation, not a resistance, though some of the manifestations give a resistance. The standard manifestations can only grant fire, cold, and lightning resistance. If the non-standard manifestations are allowed, those can be used to gain acid or psychic resistance. None of the manifestations grant resistance to thunder, radiant, or necrotic, so if the character has resistance to one or more of those elements then it either comes from some other source or s/he is doing something wrong.