Determining a system's causality using its impulse response
Clearly, for negative values of $t$, the system needs to know the future in order to determine its output. Hence, the system can't be causal.
Since the system is also time-varying (show it!), its response to an impulse doesn't say much about its general behavior, unlike it would be the case for a linear time-invariant (LTI) system. So the given system's response to an impulse being zero for $t&lt;0$ doesn't say anything at all about causality or any other general properties of the system.
Takeaway: don't use a system's impulse response for drawing conclusions about its properties before having verified that the system is LTI and can in fact be characterized by its impulse response.