DRAG pulse is for removing the the leakage, transition to unwanted states. It means, DRAG pulse assumed that more than two-level system. First, for simplicity, assume three-level system $\left\{\left|g\right>, \left|e\right>, \left|t\right> \right\}$, where resonance between $\left|g\right>\leftrightarrow\left|e\right>$ is $\omega_0$ and resonance between $\left|e\right> \leftrightarrow \left|t\right>$ is $\omega_0+\delta$. After RWA, the toy Hamiltonian becomes,

$$ \hat{H} = \frac{\hbar}{2}\begin{bmatrix} && \Omega_1 && \\\Omega_1^* && -2\Delta && \Omega_2 \\ && \Omega_2^* && -2(2\Delta+\delta)\end{bmatrix} $$