But publication itself is not the responsibility of the Secretary of State. It is the responsibility of the Legislative Reference Bureau. It is obligated to "publish every act and every portion of an act which is enacted by the legislature over the governor's partial veto within 10 working days after its date of enactment." This would presumably be on the date designated by the Secretary of State, although it is not clear that this obligation is contingent upon the designation of a date by the Secretary.
The order in Ozanne was directed to the Secretary of State. Judge Sumi held that "[t]he next step in implementation of the law would be publication of that law by the Secretary of State." That assumption was incorrect. She then ordered that "[h]e is restrained and enjoined from such publication until further order of this court."
Secretary of LaFollette has complied with that order.
But, the thing is, he had no responsibility for the law's publication. The Legislative Reference Bureau was obligated to publish the law. It's duty is mandatory and not something that the Governor- or the Secretary of State - can either mandate or stop. The LRB did this because the LRB had to do it. If District Attorney Ozanne wanted to stop it, he should have sued the LRB. He didn't.
Now I understand that people will say that the LRB should have figured out what Judge Sumi wanted and did what the DA did not ask for and she did not order and that it was not obligated to do. The law doesn't work that way. It doesn't allow state agencies to do whatever they think is right or whatever they think a judge in a case to which they were not a party would have ordered them to do had they been a party. The LRB had a clear legal obligation that was not altered by any court order and it followed it.