Hardware-assisted trusted execution environments (TEEs) are critical building blocks of many modern applications. However, they have a one-way isolation model that introduces a semantic gap between a TEE and its outside world. This lack of information causes an ever-increasing set of attacks on TEE-enabled applications that exploit various insecure interactions with the host OSs, applications, or other enclaves. We introduce Sirius, the first compartmentalization framework that achieves strong isolation and secure sharing in TEE-assisted applications by controlling the dataflows within primary kernel objects (e.g. threads, processes, address spaces, files, sockets, pipes) in both the secure and normal worlds. Sirius replaces ad-hoc interactions in current TEE systems with a principled approach that adds strong inter- and intra-address space isolation and effectively eliminates a wide range of attacks. We evaluate Sirius on ARM platforms and find that it is lightweight ($\approx 15K$ LoC) and only adds $\approx 10.8\%$ overhead to enable TEE support on applications such as httpd, and improves the performance of existing TEE-enabled applications such as the Darknet ML framework and ARM's LibDDSSec by $0.05\%-5.6\%$.