Clusters of tetracene molecules with different numbers of attached (Ar)(N), (Ne)(N) and (H-2)(N) particles (N = 1-2000) are assembled inside superfluid He nanodroplets and studied via laser-induced fluorescence. The frequency shift of the fluorescence spectrum of the tetracene molecules is studied as a function of cluster site and pickup order of tetracene and cluster species. For (Ar)(N) and (Ne)(N) clusters, our results indicate that the tetracene molecules reside inside the clusters when tetracene is captured by the He nanodroplet before the cluster species; conversely, the tetracene molecules stay on the surface of the dusters when tetracene is captured after the cluster species. In the case of (H-2)(N) clusters, however, tetracene molecules reside inside the (H-2)(N) clusters irrespective of the pickup order. We conclude that (Ar)(N) and (Ne)(N) clusters are rigid at T = 0.38 K, while (H-2)(N) clusters of up to N = 2000 remain fluxional at the same temperature. The results may also indicate the occurrence of heterogeneous nucleation of the (H-2)(N) clusters, which is induced by the interaction with tetracene chromophore molecules.