Causality of the given system
You are correct that $y[n]$ only depends on past input values for $n \gt 0$, but when $n \lt 0$, that is not the case --- then $y[n]$ is dependent on future input values, regardless of what $x$ is.

To see this:
$$
y[-2] = x[-(-2)] = x[2]
$$
so the output at time $n=-2$ is dependent on the input at time $n=2$.