Satsuki azaleas will never thrive as indoor plants; at best they will endure. They must be outside unless conditions are such that they can’t, such as freezing temps. You should also be mindful that satsuki are originally riverbank, understory trees/bushes—they thrive in bright shade with some time each day in direct sun. they do not do well in garden store soil mix, or any organic mix under most climatic conditions. Their ideal ‘soil’ is pure kanuma, a Japanese baked clay that is mildly acidic. The sooner you can get it into kanuma the better. It drains nicely so that it is virtually impossible to over water, and has the additional benefit of turning white at the surface as a clue that it’s time to water.
Forget about the rocks in the tray underneath the pot. The ‘humidity tray’ is a bunch of nonsense—the tray serves only to keep you from wrecking your wife’s sideboard by leaving water marks where your pot drains. You should water at the base of the tree, until the water drains through the pot, wait twenty minutes and then do it again. Misting is useful only to the extent that it helps cool the leaves. In temps over 80 F., fully 80% of the tree’s water uptake Is for cooling.
Azaleas need deeper pots than most other trees because their roots are sensitive to moisture balance and temperature. In your climate you might want to consider elevating the pot off of the surface upon which it sits, to provide thermal separation and air circulation. You could use a wire baker’s cooling rack, wood blocks, or whatever. For this reason avoid black or other dark pots that will draw heat from the sun.
i would suggest watering early in the morning to shield against midday heat, and then in hot weather checking again at noon. Wind can dry out your pots very quickly so pay attention to that as well.
As to the brown leaf tips, satsuki are not truly ‘evergreen’. They have a major flush of growth in spring, and a minor one about two weeks after the end of flowering. Each year they replace some of the prior year’s new growth, which begins with browning at the tips of the old leaves. Eventually those leaves fall off.
Azaleas are susceptible to fertilizer burn, so use a dilute solution of whatever you’re using, at 50% strength. Many people have great success with Miracid by Miracle Grow, administered at half strength twice a month. I prefer a fish emulsion supplemented with an iron and magnesium chelate.
if you get any kind of fungus, insect infestations or other pest be mindful that most “ides”—fungicides, insecticide, miticides, etc. become phytotoxic above 80 degrees F. In hot periods they are best applied on your way to closing the house and going to bed—even if you do them in the morning before breakfast it can still be hot enough by midday to have the same lethal effect.