Install a swale at the bottom of the slope so that it carries runoff toward a storm drain or open space. Ensure that the slope drains into the swale and that the bottom of the swale is lower than the neighbor's property. Compact the subgrade before adding topsoil.
Cover the slope and swale with topsoil and grass seed or sod as soon as possible following grade work. Plant trees and shrubs instead, if desired, but make sure drainage is not impeded. Plant trees several feet from the property line.
Water landscaping carefully and avoid overwatering. Monitor the site drainage regularly, clearing any blockages as necessary.