Well the subject line says state not province.
As for adjustments, IIRC and your using QB payroll, if you change the rate the next time you submit payroll QB will generate an adjusting entry. I think it only does it for the current quarter however. Longer than that and I would contact QB Payroll's support line and ask for help. It may be to the point where you are going to get a bill from your state tax agency anyway.