Ni(NH₃)ₙ²⁺ complexes are formed by dative bonds in which the nitrogen lone pair on NH₃ donates into an empty orbital on Ni²⁺. NH₄⁺ has no lone pair available — it has already given it to a proton — so NH₄⁺ cannot coordinate to Ni²⁺. Only free NH₃ in solution can complex.
Below pKa(NH₄⁺) = 9.25 most of the total ammonia in solution exists as NH₄⁺. The diagram uses the equilibrium αNH₃ = Ka / (Ka + [H⁺]) to compute the free [NH₃] at every pH, and all Ni–NH₃ formation constants βn are referenced to free NH₃, never to NH₄⁺ or to total ammonia. This is why ammoniacal nickel plating baths must be buffered to pH ≥ 9: at lower pH there isn't enough free NH₃ to keep Ni in solution against the very low Ksp of Ni(OH)₂.
The "total ammonia" slider above counts NH₃ + NH₄⁺ together (the practical thing you measure or add to a bath); the calculation internally splits them at every pH.