A spraying, inground irrigation system would sure not be my first choice......they are seldom programmed to deliver sufficient water at any given time. More likely juste enough to 'tickle' the plant with spray without adequate penetration to the root zone.

As early in the morning as you can manage is the best time - around dawn or slightly before. This is typically when the humidity level is at its highest so there is less chance of evaporation. And the water will remain on the foliage for the least amount of time at this time of day, reducing the chances of disease.

I'd check frequently to make sure your new tree is getting enough water, especially the first couple seasons inground. You want water to penetrate the full depth of the root zone. It may be necessary to supplement with a hose or soaker to ensure the soil is kept adequately moist (not wet).