We study tangent sets of truly self-affine sets in the plane. If a set in this class satisfies the strong separation condition and projects to a line segment for sufficiently many directions, then for each generic point there exists a rotation $O$ such that all tangent sets at that point are either of the form $O((R \times C) \cap B(0, 1))$, where $C$ is a closed porous set, or of the form $O((l \times \{0\}) \cap B(0, 1))$, where $l$ is an interval.