Effective Date for a Change in income

I’m sure I am making this more complicated than it should be as this isn’t an uncommon scenario.
However, I am getting myself more and more confused the more I think about it, and the more I read the Regs:

When a tenant is receiving HB and is working part time, paid monthly :
If they increase their hours does the change take effect from the day their hours increase or from when they receive their increased wage i.e. at the end of the month.
I was under the impression it was the date the wage was paid as long as this was the due date., however have been informed by the Authority that the date of change is the day the hours changed?
I have 2 cases at the moment and have read Reg 79 and feel that this supports my case and it appears to me it is only taken back if it is arrears of wages, and not if wages are paid when they are meant to be paid.

The 2 cases are slightly different as in one case HB is continuing at a lower rate, but in the other the increase in wages takes them off HB altogether, so unsure if this makes a difference also?
Neither claim has a qualifying benefit in payment. 

Any clarification would be welcome.

Thanks Greg