Tree's generate water as part of the respiration process (not to be confused with photosynthesis which is different). This happens at night and day.
This is relatively static day or night. Photosynthesis alters dependant on sunlight, respiration (being the process of producing energy) does not. Respiration will alter dependant on the time of year, i.e. in winter a tree may be dormant with no leaves, etc. and respiration almost stops.
You're not going to be able to generate anywhere near enough water using this method, regardless of the time of day. This is a useful survival method but that's it. do not rely on it as a source of water.
The trap you show above is likely to produce a few ml of water per day regardless of climate. You're likely going to need several litres of water per day.
I couldn't find any exact figures on the amount of water you're going to get but this wikipedia article describes a condensation trap much larger than the one you describe that yields very low volumes of water:
Condensation traps are not in themselves a sustainable source of
water; they are sources for extending or supplementing existing water
sources or supplies, and should not be relied on to provide a person's
daily requirement for water, since a trap measuring 16" in diameter by
12" deep will only yield around 100 to 150 ml per day.