Multimodal-Attributed Graphs (MAGs) organize heterogeneous data in graphs whose nodes are characterized by modalities such as text and images rather than traditional unimodal attributes. However, many representative MAG methods organize propagation around node-level states and topology-defined neighborhoods, which can obscure fine-grained modality contributions: a bounded neighborhood may contain semantically weak evidence, while compatible context need not be confined to it. To address both limitations, we propose TEAM, a modality-centric framework that constructs and encodes graph context with node-modality tokens rather than treating each node as a single interaction unit. Concretely, TEAM unfolds the local topology into a Modality Encoding Tree and performs tree-anchored semantic evidence acquisition, organizing local structural context while expanding the accessible evidence space outside the constructed local Tree. We further introduce the Modality-Source Context Transformer (MSCT), which encodes the selected node-modality tokens and coordinates interactions among modality-source groups. By retaining textual and visual attributes as separate interaction units until readout, it supports fine-grained cross-node cross-modal exchange without first collapsing them into whole-node features. Across the evaluated baselines, TEAM attains the highest reported mean on all graph-learning metrics, all three G2Text metrics, and both G2Image metrics. On Toys, it surpasses the strongest baseline by 3.37 and 2.93 percentage points in Accuracy and Macro-F1, respectively.

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