The best time is when everyone is home, morning, evening or bad weather but they can be alittle testy at that time so I give them alttle smoke first
Personally, I would not advise to smoke the bees, not sure why you would bother, but you must have your reasons, I see it as moot though.
I do mine in the morning when I know that everyone is home (this is totally dependent upon the warmth of the area though). Where I live, I can be assured that everyone is home and in their house all night long. They don't generally go out until at least 8:00 AM or a bit later, again temperature dependent.
I seal the entrance on the bottom firstly with some foam (an old mattress worked well) and then I seal the slot on the inner cover. No bees can get out to bother me. I place the pan that has the crystals in it into the colony by pulling a tiny bit of the foam away and then quickly close it back up. I vapourize the crystals. It takes to the count of 100, I pull out the basin, cool with water, place in crystals and then carry on to the next. That hive is left sealed for 10 minutes, no less. Good luck, you will kill mites by the hundreds, if they are present within the colony, fast, efficient. Mite free. Have a beautiful and most wonderful day, love our life, health. Cindi