Go to Qufim Island and follow a path down the cliff to (F-8). Be warned that a Kraken may spawn right on top of the flowers. If you are a low level, keep a safe distance until 21:32. Any time between 21:32 and dawn, use sneak to approach safely and click on the Night Flowers for a cutscene.
If attempting this quest at lower levels, it is beneficial to reach the path before 20:00 to avoid the Banshees that appear once night falls. A Goblin Bounty Hunter also runs down the path that leads to the Night Flowers and the Kraken, so be extra careful.
Note that the marker on the map is slightly east of where the actual walkway/flowers are.
You must go all the way down and around the pathway to the right of the blue marker on the map to find the "Night Flowers" at the very bottom/end of the path in a seaside cave.
After the cutscene, return to Lower Jeuno and click on Dietmund's door again (G-11) for your reward.