The authors present a model for a class of \(\mathbb{K}\)-homogeneous \(d\)-tuples \(T\) as the operators of multiplication by the coordinate functions on a reproducing kernel Hilbert space of holomorphic functions defined on an irreducible bounded symmetric domain \(\Omega\) of rank \(r\) in \(\mathbb{C}^d\), and considering \(\mathbb{K}\) to be the subgroup of linear automorphisms in \(G\) (the connected component of identity in the group of biholomorphic automorphisms of \(\Omega\), equipped with the topology of uniform convergence on compact subsets of \(\Omega\)). The description of that model allows the deduction of several properties. Namely: (i) the determination of which \(d\)-tuple of multiplication operators on the weighted Bergman spaces are bounded; (ii) a certain comparison with the Cowen-Douglas class; and (iii) unitary equivalence and similarity of those \(d\)-tuples.