Can the instantaneous frequency be always derived from an analytic signal?
This is because the phase term is changing with time at the rate of $t^2$ for the frequency ramp, and since the instantanous frequency is the derivative of the phase your result is as expected.

$m(t) = cos(2\pi f(t) t)$

$\phi = 2\pi f(t) t$

$f(t) = Kt$ for a linear frequency ramp

thus phase versus time changes at the rate of $t^2$

$\phi = 2\pi Kt^2$

and the derivative of the phase (which is the instantaneous radian frequency) is:

$\frac{d\phi}{dt} = 4\pi Kt$

(Divide this by $2\pi$ to get instaneous frequency, but the source of the 2x discrepancy should now be very clear).

See the answer to this DSP Challenge that I posted that further explains this:

Simulation of a Frequency ramp