Having the tree checked by county extension or state agriculture would be a good idea, but apparently the primary leaf buds were killed. The green buds you're seeing are secondary buds. The blackened tips should be pruned back to live wood. I would suspect the oil spray is responsible for the death of the primary buds. The past winter throughout New England was exceptionally mild, so winter kill is highly
unlikely. Unless there is a specific reason for spraying, it's not a great idea. Even the all season oils can damage tender new growth when temperatures fluctuate greatly, the application is too heavy, etc.