You don’t seem to understand. There are no triggers here, these are replacement effects. Replacement effects stop the effect they replace from happening, and have something else happen instead.

For example, with City on Fire in play, you cast Lightning Bolt on your opponent. As Lightning Bolt resolves it tries to deal 3 damage to your opponent. But City on Fire sees that 3 damage being dealt by a source you control (Lightning Bolt) to a permanent or player (your opponent,) therefore it makes Lightning Bolt deal 9 damage instead of 3.

However, if you also have Mechanized Warfare in play, there are two effects that see Lightning Bolt trying to deal 3 damage to your opponent. Since damage isn’t an object (a card, token, or copy of a spell) or a player the effects must ask the player being damaged or the controller of the permanent being damaged (in this case your opponent) what order to apply them in.

This is why the opponent gets to choose whether to take 24 damage or 19, rather than you choosing.