Lands held by private persons under possessory rights from the federal government may be included within the operation of the district, and as soon as such lands are held under title of private ownership, the owner thereof shall be entitled to receive his or her proportion of water as in case of other landowners upon payment by him or her of such sums as shall be determined by the district board and at the time to be fixed by said district board, which sum shall be such equitable amount as such lands should pay having regard to placing said lands on the basis of equality with other lands in the district as to benefits received, and giving credit if equitable for any sums paid as water rent by the occupant of said lands prior to the vesting of private ownership, and such lands shall also become subject to all taxes and assessments of the district thereafter imposed.