What happens to the colour change of an equilibrium reaction when one of the reactants begins to form a complex? (specific problem included)
Going by the right hand picture, what was formed there is the very poorly soluble and lightly yellow $\ce{FePO4.2H2O}$. A precipitate and clear supernatant liquid can clearly be seen.

If so, the reaction is:

$$\ce{FeSCN^{2+}(aq) + HPO4^{-}(aq) + 3 H2O(l) \to FePO4.2H2O(s) + SCN-(aq) + H3O+(aq)}$$

This explains why on adding the $\ce{Na2HPO4}$ the red colour of the $\ce{FeSCN^{2+}}$ complex disappears and a yellowish, flocculant precipitate appears. This is not however, as the OP suspected, a complex. It's merely an almost insoluble salt.

Some info on $\ce{FePO4}$.



A true complex would have been formed by the addition of $\ce{CN-}$, which would have led to the formation of $\ce{Fe(CN)6^{3-}}$, which has a much higher formation constant ($K_f$) than the thiocyanate complex. It's also weakly coloured and would not form a precipiate. The reaction would have been:

$$\ce{FeSCN^{2+}(aq) + 6 CN-(aq) \to Fe(CN)6^{3-}(aq) + SCN-(aq)}$$

The solution would have evolved from bordeaux to weakly amber/red.