I logged after a few days out and I was able to collect the 10 CSC rewards on both Kumos and Legacy.

I noticed the bar on Legacy only goes up if you finish quests on Kumos. So I finished my Kumos quests and collected the rewards.

Later, I finished all my Legacy quests (except for Major Drills and Sarah) and ended up being able to also collect 10 CSC here on Legacy by clicking those reward buttons.

I am unsure if this is intended, and I cannot replicate it right now because it's very time consuming! But I'm leaving this to say it happened to me, and I'm not sure if it was intended.

That only happens on the first time. From now on you can only collect Kumos quest CSC on Subeta, however there is a waiting time :-(

https://subeta.net/forums.php/read/944173/Quests-with-Kumos-infobar-amp-no-Kumos-CSC