Step 1: We need the name of the joint disorder that arises as an immune reaction to tuberculosis rather than from invasion of the joint by the organism.
Step 2: That entity is Poncet's disease, an aseptic reactive polyarthritis seen alongside active TB at another site. Synovial cultures and tissue stains are negative for the bacillus, and the arthritis resolves once anti-tubercular drugs are given, confirming its reactive nature.
Step 3: Excluding the rest: spina ventosa refers to TB of the small tubular bones (dactylitis) in children with actual bacillary infection of bone, while Pott's disease denotes tuberculous involvement of the vertebral column. Both are direct infections, so neither matches a reactive arthritis.
Step 4: Thus the reactive tubercular arthritis is Poncet's disease.
\[\boxed{\text{Poncet's disease}}\]