Seasonal jobs that might turn permanent - 18 weeks in

A staffing agency says some roles convert to permanent after 9 weeks. There are 9 people counting on me, so I am trying to be careful. The pay is hourly with weekly deposits. Has anyone been converted to permanent?

Thanks for writing this out. I went through something close to it 8 months ago, and it got easier once I kept a simple log of every call and form.