Causal and Non-causal filtering. Strange behavior
the output causal filtered signal inside the red box seems to be very uncorrelated with the zero-phase filtered signal.


So let's look at this statement. Suppose the original, unfiltered signal is $x[n]$. Filtering this using filtfilt with a filter with impulse response $h[n]$ gives:
$$
y_{ff}[n] = h[-n] \star h[n] \star x[n]
$$
and filtering with just filter is:
$$
y_f[n] = h[n] \star x[n]
$$
so
$$
y_{ff}[n] = h[-n] \star y_f[n]
$$
Regardless of what $x[n]$ is, the 'correlation' between $y_f$ and $y_{ff}$ will look like the anticausal (perhaps anticausal + constant term) $h[-n]$.