The study of epidemic spreading in node-property heterogeneous adaptive network shows that node-property heterogeneity can greatly increase the epidemic threshold, and the initial network can adaptively self-organize into a more robust degree heterogeneous network structure. The difference in epidemic spreading between homogeneous and heterogeneous node-property adaptive networks is of great importance for understanding the threshold increasing in the heterogeneous node-property adaptive network. In this paper, we study the transient spreading process in the heterogeneous node-property adaptive network. In order to capture the core-periphery structure in the network, we define two hierarchical structure indicators. When both indicators are of large values in the network, not only is the network of strong core-periphery property, but also less susceptible nodes are more likely to be in the core area of the network. By combining them with various network structure properties, such as the average degree ratio and static threshold of transient network, we analyze the evolution of network structure and show the self-organizing formation process of robust degree heterogeneous structure by numerical simulations. We find that the threshold increase is basically due to the formation of core-periphery structure, where the less susceptible nodes are more likely to be reallocated to the core area of the network by rewiring. In view of this, we propose a new preference rewiring strategy. The results show that the new strategy can increase the epidemic threshold by faciliating the formation of core-periphery structure, which verifies the correctness of the transient network structure analysis. It not only helps to deeply understand the epidemic spreading process in the node-property heterogeneous adaptive network, but also provides new ideas for putting forward the strategy of controlling epidemics.