Natural migration to UC from ESA/ Housing Benefit

I have a query regarding possible change of circumstances and how it might affect me and would appreciate any advice.
I claim ESA (IR) and am on PIP enhanced mob and standard rate care.
My daughter who is over 18 might be moving back in with me in the new year and I will have to inform both ESA to stop my severe disability premium and local council as I pay bedroom tax on one extra room. Obviously I will no longer have to pay Bedroom Tax and non dependent deductions aren't an issue due to my being on standard rate PIP care.
I am pretty sure as my ESA claim would not be ending or changing to a different benefit that won't prompt a need to claim U/C.
However, the Housing Benefit I receive will rise by approx 13 pounds so I would be entitled to full H/Ben as it were.
Again, there would be no need for a new claim to Housing Ben merely an adjustment to the amount paid.
I notice the government advice and that posted on entitled to and most welfare websites says the general rule of thumb is that....... "In general, natural migration could be triggered if entitlement to your current benefit ends (prompting a need to claim a new one) or you become entitled to a different or extra benefit. It shouldn't happen when you make changes to benefits you are already claiming."
The phrase I am uncertain about here is " extra benefit" Could that mean an extra benefit on top of a benefit you are already receiving or does it mean extra amount as in the 13 pounds extra taking my Housing Ben to full entitlement because I would not need to pay the bedroom tax any longer ? Also, the lady at my local authority suggested that an extra adult moving into my house, ( my daughter is 19) might trigger a need to claim U/C although she said she wasn't sure. In Fact she didn't seem to know what she was talking about . I would be grateful of any clarity on this as the government lists scenarios, though not exhaustive, of when a change might trigger a need to claim U/C. The scenarios I mention weren't on there.
Any advice would be much appreciate as I was hoping to be one of those listed for managed migration sometime in the future as opposed to so called natural migration.

Thanks for that Gordon I just worried that removing the bedroom tax I have had to pay might mean a fresh housing benefit claim, as it involves my claiming the full amount again, ( the extra 13 or so pounds) and thus a rise in housing benefit they will have to pay me. From what you say, obviously not Thanks again....