From reading the post, it would seem that whether you gained an ability from your current class or from another class will no longer have any effect on that ability. This does not mean that you can use cross-classed abilities at full strength. Instead, a class will gain traits which enhance their use of their own abilities, such as PUG gaining a trait that says, "Hand to Hand Damage Increased." Conjurer could gain a trait that Increases Healing Magic Potency (or more likely, a few traits with this effect, throughout their leveling).

In short, ability potency and recast will no longer vary based on the class equipping them. Instead, you will receive traits that give you bonuses for using abilities from your currently equipped class.