Basic question about chirp signal
I dont understand the definition of the chirp in the link you provided (perhaps chirp in frequency domain?), but maybe the following explanation could help.

In general, a linear chirp with a varying frequency given by $$f(t) = \alpha + \beta t$$ is defined by $$ x_1(t) = e^{2\pi j (\alpha t + 0.5\beta t^2)} $$

In that case, the phase of $x_1(t)$, the signal in time-domain, is indeed parabolic and the magnitude is constant and equals to 1.
Now, I am not familiar with python, but the chirp function in matlab produces a real signal rather than complex one. That is $$ x_2(t) = \sin(2\pi  (\alpha t + 0.5\beta t^2)) $$ In that case, you will get different results. However, you can use the Hilbert transform (I guess this is in python) which, given $x_1(t)$ will produce $x_2(t)$ using fft.