Does changing the frequency of a wave cause a change of the phase of the same wave?
Let's assume your two sinusoids are at the same phase, $\phi_0$, at $t=0$ and you change the frequency of one of them at exactly that time.

The phases as functions of time, for $t \ge 0$, for those sinusoids at the two different frequencies are

$$\phi_1(t) = 2\pi f_1 t + \phi_0$$
$$\phi_2(t) = 2\pi f_2 t + \phi_0$$

And the difference between those phases is

$$\psi(t) = \phi_1(t)-\phi_2(t) = 2\pi(f_1-f_2)t$$

So the phase difference between them is a function of time and the difference between the two frequencies.