Hi, thank you for the clear question; the contribution tree shows a tree / non-looped view of the calculated impacts for the connected life cycle you modeled. If you apply allocation for a process with two products / intermediate flows, you get "rid of" one of the products, thus this will indeed disappear in the view as it does not have impacts. If you do not apply allocation (it does not matter whether physical or economic), you have both products with impacts and thus two supply chains that are duplicates indeed. An intermediate flow is also a product, maybe not for the end consumer but for the process producing it, thus for the modeling and for whether to apply allocation or not, there is no difference.
What you should do? Apply allocation whenever you have more than one function (product produced, waste treated) in a process, and use the allocation type foreseen in goal and scope ideally -> 1 no (assuming in g&s you did not say no allocation to be used), 2 two input paths but also double counting as this is what no allocation does 3 any place where more than one product appear.
Success!
edit: to not complicate things further, I left the system expansion / avoid allocation options out of the discussion here; these would come first.