It's nothing to do with split tickets; train companies such as Avanti and Northern are very keen to avoid paying Delay Repay and will claim another operator is responsible wherever they think they can get away with it. This applies regardless of whether it's on a through fare or a combination of fares.
There are plenty of examples of the exact same issue occurring on through fares.
It sounds like Northern are liable, however it is difficult for us to help, when it's written in this style, rather than listed in a format that an itinerary would typically appear.
When people are seeking advice regarding itineraries, delay claims, etc, it is a good idea to list the planned itinerary in list format. After the journey, the actual journey times can be listed in the same format, with notes regarding which trains were delayed/cancelled.
Like this, please:
This will help us to help you; thanks