I took a little look into this and based on that I think you are correct that Service Ontario was already significantly privatized prior to this move (which I'll admit I wasn't aware of), but it has not always been completely private.

Here are excerpts from a 2014 post from OPSEU (https://opseu.org/information/general/serviceontario-the-straight-facts/9956/):

The McGuinty government likes to claim that two-thirds of ServiceOntario is already privatized. While two-thirds of ServiceOntario’s retail counters are privately run, claiming that two-thirds of ServiceOntario is already privatized is a gross oversimplification. This claim ignores the publicly run backbone of the organization. The components of ServiceOntario directly operated by the province include:

• 87 public counters across Ontario
• 9 contact centers that answer 10 million calls annually
• Online services handling close to 10 million transactions annually
• Mailrooms processing 22 million items annually

ServiceOntario employs about 2400 people that are direct employees of the province. OPSEU represents approximately 1850 of those employees.