I'd go with the 15 minutes (or more) 3 times a week. Watering only a few minutes doesn't allow the water to soak into the soil very deep. That in turn causes the roots to be very shallow, something that's not all that great. A deeper watering helps the roots to grow deeper as well, which means the plants will be more likely to NOT fall over every time the wind blows, they'll be able to reach more nutrients and won't get stressed as easily.
Hope that helps some.

Kevin

If the previous owner designed the system, one would think his advice would be hard to beat. But 4 minutes a day just sounds wrong. However, there really is no rule of thumb that can be given because there are too many variables. A major one is the output of the emitters. Some emitters put out only ½ gph. Others might put out ten or twenty times that much. A few other variables are:

1. soil porosity
2. drought tolerance of the plant material
3. exposure: full sun? filtered sun? half-day shade?
4. seasonality and current weather: hot and windy? into the monsoon season?

As Kevin pointed out, the conceptual principle is to provide DEEP watering. Frequent shallow watering is false economy and a waste of water. Better to save money by watering deeply and less frequently. When I lived in southern Arizona, I never ran drip systems for less than an hour, and seldom more than once a week, but I designed my own system with low-output emitters, used mostly drought-tolerant plants, and knew what I wanted. You will have to experiment. Your plants will let you know when they are water-stressed. Overwatering produces weak growth, so I would be conservative.

"The owner said that he ran the drip system for 4 minutes daily."

For almost any low water use plant, it's way too little, and way too often ... this kind of watering keeps the roots close to the surface where they are suceptible to drying. It also keeps the roots too wet for many succulents.

You have to shift the watering schedule slowly so you don't kill the plants: change to 10 minutes every other day for a month, then 15 minutes every 4 days for the rest of the hot season.

During the cool season, once a week is usually enough. I don't worry about tracking rain: it's a bonus for the plants.

Next summer, you should have no problem with 15 minutes every 4 days.

As the bougainvillas get larger, they will need even more infrequent, but deeper watering.

How many drip circuits do you have?

Most drip systems are set up with one-gallon-per-hour emitters. They look like little flags or perhaps round cylinders. One gallon of water will moisten about 1 cubic foot of soil - just about enough for a small 1 gallon plant. Running a drip system for 15 minutes with these emitters will only deliver a quart of water which is way to little for a plant.

The motto for watering is "deep and infrequent". This will encourage deep roots and keeps moisture in the root zone for a longer period of time. It also allows oxygen exchange at the roots which is essential for metabolizing nutrients. Deep watering also pushes accumulated salts (the white stuff you see on terra cotta pots or faucets) down below the roots. Salts, especially sodium, can kill plants.

If your plants haven't been through a summer yet you'll need to water at least twice a week for two hours each time. Trees especially will benefit from the deep soaking. If you have turf run your sprinklers twice a week for 15 - 20 minutes.

Of course if you have adjustable emitters that put out more than one gallon of water, you may not need to water quite as long.

This watering schedule works. U of A research and horticulture experts recommend it. I've used it in my own landscape and my plants are healthy and flourishing.

Here is a link that might be useful: Landscape Watering Guidelines

Thank you all for your advice. I tried to run the sprinklers for 10 minutes, 4 times a week. Everything wilted. I am about to lose a salt bush? There are little trees coming up under the street tree. Since it drops so many seeds I thought they were seedlings. When I dug down I found that they were sprouts from a main tree root about 2-3 inches below ground. That's the result of the daily watering. When it cools off I will try to switch slowly over to deep watering again.