In response to criZp's posts, not quite. Now that I've learned more about it, here's a more in-depth explanation.
Units do not have Modifiers attached to them directly. They are either given Abilities or Promotions. The Mamluk, for example, is given its healing after everything as an Ability, but the Ground Crews Promotion for Air Fighters is, well, a Promotion. The difference is that Promotions are what you get when you gain a level, no more, no less. Abilities are given for just about any situation where you need to attach a modifier to a unit. So, the way to properly do it, I think, is to make a civilization trait with the ModifierType of something like PLAYER_UNITS_GRANT_ABILITY, set that ability to have the Modifier of a Type 'MODIFIER_PLAYER_UNIT_GRANT_HEAL_AFTER_ACTION', and then set that ability (in the TypeTags table) to be part of the classes which you want to give it to, so CLASS_MELEE, CLASS_RECON, etc. It won't effect anything of a class other than what you define in that table.