Are you saying all spells that list cone as the area of effect are eminations from the caster? I can't think of a counter example, but I wasn't aware that this was an implicite part of the rules.
An emanation is something different, but it is true that "When you cast a spell with a cone area, the cone shoots away from you in the direction you designate. A cone starts as a point directly before you, and it widens out as it goes." (PHB p. 149)