Disability premium in esa

I’d be very grateful for some advice on this one. I’ve been given so much conflicting information ( in job centre and on esa helpline), I really would like to find out the correct answer.

I had good news yesterday my dla to pip went positively. 10 Pts care and 12 mobility, and decision maker agreed till 2021. I had previously got low care and high mobility under dla, which didn’t entitle me to disability premium under esa, so I never claimed income related, as I believe it wouldn’t have benefited me, due to a small pension I have. The decision was made yesterday on my pip but is only effective as of 13/12/17.

Using entitledto it now looks like I can get considerably more claiming income related ( due to the disability premium) So far so good. The thing is my job centre goes to universal credit at the end of the month, and under universal credit, if not transitionally protected, I will lose £2500 a year ongoing.

Now the reason for my query is this, the job centre and helpline tell me that as I already get esa contributory they simply make a change in December to add on the fact I now get pip care, which enables me to get the income related disability premium. However this is not tying in with what looks like a well researched document www.southampton.gov.uk/benefits-welfare/...niversal-credit.aspx
Which shows it as a new claim for universal credit when esa it is being added to cont. under uc disability premium isn’t available, as we know.
What I want to know is when I put in my esa3, will the date I Notify them of the change ( or the decision makers decision) be significant or the effective date of my pip award, be dominant ( this is after the introduction of universal credit in my area). Under normal circumstances this wouldn’t be such a big deal but the amount for the forseable future, in my circumstances is massive, in fact more than the care allowance itself.
Any advice / opinion appreciated.

Thanks for that Gordon, that’s what most people are telling me, and it’s reassuring.
What I couldn’t understand was on the very last item on the attachment I sent
www.southampton.gov.uk/benefits-welfare/...niversal-credit.aspx The very last item says it will trigger a compulsory change, so I just wanted to make absolutely sure. Many thanks.