The definition of the variant trait is all we have to go on here. I believe the relevant part of the trait is actually the idea that the tiefling is healed by both positive and negative energy - nothing is said about any other effect. And, as you have found, the defintion of Channel is a little rubbery. So, I can only see two ways to treat this.
The change is intended to only alter the clerical Channel Energy ability, when it is used to heal. No change is made to the way Channel Energy to harm works (meaning the tiefling would be harmed by a negative Channel to harm, but not a positive Channel to harm), nor is any change made to the way Cure or Inflict spells work (meaning a Cure spell will heal, and an Inflict spell will cause damage). Spells that heal without either type of energy (such as Regenerate, or Celestial or Infernal Healing) are unaffected, as is Natural Healing.
The change is intended to change the way a tiefling reacts to all positive and negative energy. The tiefling is healed by any effect that says it heals via positive or negative energy, regardless of whether channeling is mentioned. This would then mean that the tiefling would be healed by both cure and inflict spells. Spells that heal without either type of energy (such as Regenerate, or Celestial or Infernal Healing) are unaffected, as is Natural Healing.
In the absence of anything definitive, expect table variation, and a final ruling by the individual GM.