If the system only covers the beds, then you probably don't need to do much more than 20 minutes 4 days a week. Make sure that you set it to go off at night or early in the morning so that the water will be asborbed by the plants and the ground. Watering during the day will only lead to evaporation of most of the water. Pay attention and make sure that none of the plants are getting waterlogged or constantly sit in a puddle. None of the plants you've listed are big water-hogs, so you could even cut back to 3 days a week unless it's been hot and dry long enough for the plants to start showing signs of distress.
For the trees, you want long, infrequent waterings. Remember that tree roots generally extend to 3x the diameter of the crown. Most of the water from 20 minutes of sprinkler action is going to get absorbed by the plants above, and tree roots generally travel much deeper than plants (6'-18'), so make sure that they're getting water at least once or twice a month. Trees won't send roots under a sidewalk (unless you build the sidewalk on top of them) or anywhere else where there won't be any water for them, so use that as your guide.
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