Macroalgae, or seaweeds, are colonized by a microbial community which can be directly linked to their performance. This community is shaped by an interplay of stochastic and deterministic processes, including mechanisms which the holobiont host deploys to manipulate its associated microbiota. The Anna Karenina Principle predicts that when a holobiont is exposed to suboptimal or stressful conditions, these host mechanisms may be compromised. This leads to a relative increase of stochastic processes that may potentially result in the succession of a microbial community harmful to the host. Based on this principle, we used the variability in microbial communities (i.e., beta-diversity) as a proxy for host influence within the invasive holobiont Gracilaria vermiculophylla during a simulated invasion in a common garden experiment. Our results demonstrate that at elevated temperature, host performance decreases, while the probability to develop disease and epibiota dispersion rise. In a common garden, non-native populations perform overall better. At the optimal temperature (15C), epibiota dispersion (beta-diversity within populations) does not differ between native and non-native populations. However, thermally stressed (22C) epibiota in native populations disperse substantially more compared to non-native populations. This suggests that epibiota associated with holobionts from native populations under thermal stress are more prone to stochastic processes than holobionts from non-native populations. We argue that this pattern in beta-diversity reflects an increase of deterministic processes acting on epibiota associated with non-native hosts, which in the setting of a common garden can be assumed to originate from the host itself. Therefore, these experimental data suggest that the invasion process may have selected for hosts in which mechanisms influencing associated epibiota are more stable during stress. However, future studies are needed to identify the underlying host mechanisms.