I am a Firesoul Genasi with Extra Manifestation (Water) and Extra Manifestation II (Earth). As I understand it, in order to get the passive bonuses that come with each manifestation (i.e. +1 Reflex and resist fire for firesoul, +1 racial bonus to both Fortitude and saving throws for earthsoul), you must be using that manifestation. Does this also hold true for the racial power (Firepulse for Firesoul, Earthshock for Earthsoul)?
The racial powers and bonuses a genasi gains are a direct result of the elemental soul they are manifesting.
Each manifestation has a description of what you gain when using that manifestation. Both the passive bonuses and the powers are listed in this description so you only gain these benefits if you are using that manifestation.
This is backed up by the fact that the Extra Manifestation feat allows you to switch from one to another rather than giving you the benefits of other manifestations in addition to the one you're already using and, as @Oblivious Sage pointed out, the Double Manifestation epic-tier feat, which only then allows you to manifest 2 different elements at once so long as you already have access to them (via the Extra Manifestation feat).
If merely having access to more than one manifestation allowed you to gain it's benefits, the Double Manifestation feat would be unnecessary and/or both of these feats be worded in such a way that told you what extra benefits you would gain.