 Solution

The negative activation volume is consistent with an associative substitution pathway: an incoming donor of the tetradentate ligand approaches square-planar Ni, giving a five-coordinate transition structure/intermediate before a donor of an original chelate leaves. Successive donor substitution and chelate closure give the tetradentate N${}_2$O${}_2$ complex. Proton transfers convert the incoming phenolic groups to coordinated phenoxides while releasing the original ligands.

With acid/base forms written explicitly, the net ligand exchange is $\mathrm{Ni}({\mathrm{L}}_{\mathrm{a}}{)}_2+{\mathrm{H}}_2{\mathrm{L}}_{\mathrm{d}}\to \mathrm{Ni}({\mathrm{L}}_{\mathrm{d}})+2H{\mathrm{L}}_{\mathrm{a}}$. The connected four-donor ligand benefits from the chelate effect.

The bulky N-tert-butyl groups in $\mathrm{Ni}({\mathrm{L}}_{\mathrm{c}}{)}_2$ hinder precisely the close donor approach needed for that associative route, and the starting tetrahedral geometry must reorganize to accept the planar tetradentate ligand. Consequently exchange can be too slow to observe under the stated conditions. Failure to observe a new product is a kinetic observation; it does not establish that all tetrahedral nickel complexes are inert or that the tetradentate product is thermodynamically impossible.