It means if a company were to use a third party to collude on wages, it's colluding.
I can certainly see ways a third party company could help allow companies to engage in anticompetitive behavior. IANAL, but I expect proof of anticompetitive behavior resulting in harm to workers would need to be demonstrated. For instance if the third party software used previous pay data from a different employer (not disclosed by the applicant) to keep a salary below market rate.
No. The third party is the one colluding in your example, assuming the facts there are the same here: one software vendor, all the companies in a city are using it, software is driving wages in a direction profitable for companies and worse for employees of said company.