The fluidity of carbon dioxide leads to cross-border carbon exchange. This paper explores decentralized decision-making and centralized management modes for regional carbon managing strategy under carbon market mechanisms. The evolutionary trends and impact of management strategies on each region are explored, and market conditions for achieving specific carbon governance effects in regions are analyzed. The results demonstrate that 1) carbon market price fluctuations have a significant regulatory effect on regional carbon stocks and emission reduction behavior, and can affect the dominant characteristics of regional emission reduction effects under the two modes. 2) Increasing the duration of the game can significantly reduce the growth rate of regional carbon production and control the downward trend of regional carbon absorption. Moreover, when one party almost ignores the local pollution level, the carbon management strategies of the other party are consistent under the two modes. 3) The dual pressures faced by downstream regions regarding carbon emission reduction and economic growth can be effectively alleviated under the centralized management mode. The conclusion of this paper provides policy suggestions for regions to formulate emission management strategies and to guide efficient governance of interactive carbon pollution in cross-border carbon pollution processes.