Why do you get instantaneous phase by calculating correlation with a carrier signal?
This is the analytic signal. See wikipedia for better details.

Basically you are taking the carrier correlation, $f(x)$, and its Hilbert transform, $(h \ast f)(x)$ and combining them into a single complex valued signal, the analytic signal

$$f_A(x) = f(x) - i (h \ast f)(x)$$

which can be written as the complex exponential

$$f_A(x) = A(x) e^{i \phi(x)}$$

Why this is useful is that it performs a split of identity into seperate amplitude $A$ and phase $\phi$ components. Actually the Hilbert transform requires the entire signal to compute, but because you know the function of your signal already you only need the one sample.To localise the phase, you would use a bandpass filter.