Canonical Rectangular Modulation
Your understanding is not correct. The baseband processing maps the message to a complex-valued signal

$$x(t)=R(t)e^{j\phi(t)}\tag{1}$$

or, equivalently, to an in-phase component $I(t)=\text{Re}\{x(t)\}$, and a quadrature component $Q(t)=\text{Im}\{x(t)\}$. It is not clear from the figure how $R(t)$ and $\phi(t)$ are related to the message signal $m(t)$. The modulated signal is constructed by multiplying $(1)$ by a (complex) carrier, and taking the real part:

$$s(t)=\text{Re}\{x(t)e^{j\omega_ct}\}=R(t)\cos(\omega_ct+\phi(t))\tag{2}$$