Unsurprisingly this is a question that has come up before, and the answer is always that it does work. Based on these other posts Nyxbloom Ancient should also make 9 mana for everyone in case the client is not doing that as well.
Curious at the labeling on this one. Both Mana Reflection and Nyxbloom Ancient both have rulings that clarify they don't make mana themselves, they only modify the amount of the generated by the source. Nothing about this interaction suggests it shouldn't work.
Mana Reflection doesn't produce any mana itself. Rather, it causes permanents you tap for mana to produce more mana. If the mana ability of that permanent puts any restrictions or riders on the mana it produces, that will apply to all the mana it produces this way.(2020-08-07)
Nyxbloom Ancient doesn’t produce any mana itself. Rather, it causes permanents you tap for mana to produce more mana. If the mana ability of that permanent puts any restrictions or riders on the mana it produces, that will apply to all the mana it produces this way.(2020-01-24)