Hello Joki,
So in order to do update your scene reflections when using a dynamic light the moves from day to night as you described you will need to do some Blueprint scripting.
Open your level Blueprint and right click in an empty space. Uncheck the checkbox that says “Context Sensitive” and type “Recapture Sky.” Use this node in conjunction with your level to recapture the sky at a certain point.
Be sure to read the thumbnail warning displayed when you hover your mouse over the node. It lets you know this is a costly procedure!
I hope this gets you the results you are looking for.
Thanks,