The assessment, collection and return of drain taxes for any work done under this chapter shall be made in the same manner and under the same provisions as in this act provided for drain taxes assessed, collected, returned and enforced in the first instance: Provided, That in all proceedings involving subsequent assessments, the drain commissioner shall furnish to the supervisor of each township containing parcels of land subject to such assessment the names of the owners of record of such parcels as of the date of the assessment.