What is the meaning of negative second for a Morlet wavelet?
Continuous wavelets with symmetric envelope are often described, by convention, on a symmetric time interval: $[-T,T]$. The Gaussian being of infinite support, this means it is truncated.

This is only a matter of convention, as the wavelet shape is translated and dilated over the whole time axis. One could thus specify as well the same wavelet on the interval $[0,2T]$.