It sounds odd to me as well with the 'been' before 'used to'. One interpretation would be the writer is using the past perfect continuous -("had + been +'used to') with the 'used to' being the continuous action. ie. The writer is thinking of the 'used to' as an experience occuring over a period of time. Another interpretation is the writer is using a passive voice by using 'been'. Maybe someone else has the right or better answer ...

I'm not sure where you found that sentence bit it should read "It was noticed that they wagged their tails AT him, in the same way as the other dogs used to with Mr, Jones." Even now the sentence is a bit clumsy.