Do the DWP need to attend a tribunal to appeal the judges decision

No, they don't.

You'd have to ask the DWP why they ask for statements of reasons in some cases and not others, and very occasionally appeal to an upper tier tribunal.

The answer to the OP's question is that DWP do not need to have attended the hearing in order to ask for an SOR and maybe appeal.  Many members have reported that DWP have asked for an SOR where they have not attended the hearing.