NHI - I’m not sure if I need to enroll?

I finished my contract with my previous job at the end of July and started a new job on September 1st. When I check before it said I would need to do anything for NHI (I paid my pension payment for the month of August between jobs). But now I’m seeing that I should’ve enrolled in NHI back then for that month??

It’s visa renewal time so I don’t want it to jeopardise my renewal. Anyone have experience with this?

I’m going to my ward office to find out if there’s any outstanding payments.