The mushroom spores may have been in your soil or in the bark mix. What causes them to germinate is mloisture and darkness.
Use of a drip sysltem to water the flower bed is probably impractical. Raising the canopy of the treeif it is less than your shoulder height may be the answer. that would allow more sunlight in the area. However, if you planted shade plants that maymean they are doomed. Watering around dawn may be the best answer for you as it would allow the beds the longest time to dry out before sunset. I recommend thatif you are not currently doing that.