What app are you using to do this? You name a custom app (which I wrote) in the title of your thread, but nothing in your post says for sure. The built-in Motion Lighting app sounds like it can do all you're asking, so (as much as I like my app), I'd consider starting there.
Normally a "delay" option in this kind of app is the number of minutes to wait after motion becomes inactive before turning off the light, but this will depend on the specific app and setting you're talking about.
Here is what I tried to configure. In fact as I said, I would like that when it is in "night" mode and a movement is detected, that my led strip lights up for say 10 minutes. Then for 30 seconds that the light is reduced to turn off.
Then I would also like if we are not in night mode, but the number of "lux" is below a certain level. (I suppose I only have to enable the lux restriction) That the led strip lights up with the same conditions if it is not already on.
My recommendation would be to configure the settings on the "main" screen to do what you want to happen most of the time, which I think would be turning on the lights when there is motion and lux is below a certain level. Most of that can be done with the first group of settings that you see:
You will also need to look at the "Restrictions" sections towards the bottom to get the lux thing:
Finally, you'll need to turn on the "Configure exceptions per mode" option (which it looks like you already did in your screenshot above), then configure Night mode as you want. Maybe something like this:
For all of these, you can use whatever settings you want. I think the UI is self-explanatory with what the settings do, but let me know if you have any questions! For some of this, you can play around to figure out what values you want for that particular setting (maybe 10 minutes instead of 1 minute in my example, and your lux value will depend on what your sensor reports and what you want).
That is the standard hue/saturation/brightess (HSB or HSV--Hubitat calls it "level" but it's not HSL) color model, which is what Hubitat uses and about which you can probably find more information with a search. The only caveat is that by default, Hubitat's hue model goes 0-100 instead of 0-360 like the standard model usually does, so you might need to do basic arithmetic to convert values you find elsewhere.