@gkraigher Is correct. Mana abilities may be both activated or triggered: https://mtg.gamepedia.com/Mana_ability
I think Mana Reflection works slightly differently than you say, @gkraigher. From the release notes:
If multiple replacement effects would modify what mana an ability you control produces, choose one to apply. After that, determine if any others are applicable. A replacement effect can't apply to the same event more than once this way.
So if you tap a land that would normally produce one mana, you would apply Mana Reflection first as it's the only applicable replacement effect initially. You then check and see that Damping Sphere is now applicable, so the mana is reduced to C.
If you tap a land that would normally produce two mana, you have two possible replacement effects to choose from initially, and then the second is applied. You can either apply Mana Reflection first and end up with C after Damping Sphere, or apply Damping Sphere first and end up with CC after Mana Reflection.
That's my take on it. Maybe a judge can chime in? It kinda looks like this thread is going to devolve into another B&R spat, but I hope we get a ruling before this gets buried.