I don’t have enough data to answer that question but when I were bouncing between two tiers I would had collected the loot as soon as the chest were completed if the time required to reach the next tier would have prevented me to start filling the next chest.
If the new chest would have spawned in my sleeping time I would have opened the chest after reaching the best loot available, but as for titans I guess that with a good starting rolls the numbers would be better than the quality.
When I have my chest filled and it is not yet in platinum or diamond, I wait a couple of hours (on the same day) to win a couple of more raids before I can open it in diamond so the rewards are way better! Same goes for gold vs platinum, bro (as I recall)
Since we are mentioning the wanted: heroes chest, I think it is fair that when battling against f.e. heimdall / mother north / alberich, you sometimes need to finish off the same heroes. So, defeating them twice, should count as twice, not one…