If a spell (typically a minion) "must be cast" to a certain location it is an additional restriction; you still must also follow normal casting restrictions for minions, e.g. to a site you control.
For example, must be cast submerged and also to a site you control. and must be cast to your avatar's location, and also to a site you control. Minion spells cast by must be cast to its location and also to a site you control. If the Omphalos was somehow on your opponent's site, the Omphalos wouldn't be able to cast minions to its location unless you could somehow cast minions to your opponent's site due to some other effect.
Note that if you summon a minion directly to the realm without casting it, e.g. or , then casting restrictions do not apply. (Summoning restrictions still apply.)