What do the weather providers themselves say was the rainfall amount? If dark sky or whoever is recording 0.03” of rain then Netro has to honour that

You mean a recurring program? If smart mode is set and rain forecast is above the threshold set in settings it should skip that day and the day before by default - however the default threshold is 20mm which is quite a lot of rain so you might want to lower it and maybe set it to only skip the day it rains 

It opens when it next connects to the internet (by default every hour) - you have to wake it up by pressing and holding the button on the pixie if you want it to respond immediately. Manual run seems to be designed more for testing rather than actual use, you’d want to set the schedules to do the watering as they are stored in the unit and don’t need internet connectivity to run