An employer shall be liable for compensation to an employee of a contractor or subcontractor under the employer who is not subject to this chapter, or who has not complied with the conditions of s. 102.28 (2) in any case where such employer would have been liable for compensation if such employee had been working directly for the employer, including also work in the erection, alteration, repair or demolition of improvements or of fixtures upon premises of such employer which are used or to be used in the operations of such employer. The contractor or subcontractor, if subject to this chapter, shall also be liable for such compensation, but the employee shall not recover compensation for the same injury from more than one party. The employer who becomes liable for and pays such compensation may recover the same from such contractor, subcontractor or other employer for whom the employee was working at the time of the injury if such contractor, subcontractor or other employer was an employer as defined in s. 102.04. This section does not apply to injuries occurring on or after the first day of the first July beginning after the day that the secretary files the certificate under s. 102.80 (3) (a), except that if the secretary files the certificate under s. 102.80 (3) (ag) this section does apply to claims for compensation filed on or after the date specified in that certificate.