You have two different definitions of $X(t)$.
$X'(t)=XX(t)*e^{(j2\pi ft)}$ is the tidy theoretical shorthand way to express $X(t)$ -- but note the prime.
The real-valued version is $X(t)=XXi(t)\cos(2\pi ft)-XXq(t)\sin(2\pi ft)$
The difference is that $X'(t)$ does not have any energy in $\omega < 0$, where $X(t)$ has energy centered around $\omega = 2 \pi f$ and $\omega = -2 \pi f$.
The assumption is that $f$ is much greater than the bandwidth of $XX(t)$, so that when you recover a version of $XX(t)$ from $X(t)$ using I/Q demodulation, filtering out the components around $2f$ is trivial. When this assumption holds, you can treat the inphase and quadrature components as the real and imaginary parts of $XX(t)$ for the purposes of processing the signal.