In order to ensure a proper job is done, the answer is yes they do. it could be done without doing so but would be a poor effort.
The roof should be stripped to half way across the dividing wall of the two properties, the slates cut so that the bond of the slates becomes 1 slate - full slate - 1 slate - and so on up the dviide. Then a GRP board should be installed between the 2 roof types to carry any potential water ingress into the gutter, then seal (commonly with cement) the tiles and slate.
That is the most effective way of doing this.
Other ways, including taking the new roof a few inch short of the dividing wall can cause issues to both properties (leaks, damp).
Any good, reputable roofer can do the jobs properly and not leave any visible indication of disturbance. In fact, the bond fitted properly should, to a small degree, benefit your roof (albeit only at the divide).
Hope you found this helpful.