Alkyl chain substituent has higher preference than benzyl substituent? The compound in question, and the name generated by ChemSketch:



I have looked at relevant (outdated) documentation for naming of substituted amines. I understand tertiary amines are named as: $\text{N-alkyl}_1\text{N-alkyl}_2\text{alkyl}_3\text{amine}$.

Now, I am confused at the first point: when we have to select the parent carbon chain. For this compound, I would have selected "benzylamine" as the parent chain, as it obviously has more number of carbon atoms and more unsaturation than both methyl and propyl. Thus, my preferred IUPAC name would have been "N-methyl-N-propylbenzylamine". 

But, for some reason "propane" is the main carbon chain here instead. So, what is the logical reasoning for the naming these tertiary amines?
The longest carbon chain is the base name. Benzyl has a "one carbon chain". Compare the two structures below. In the top example, the butane chain, even though it bears a phenyl group, is the main chain. On the bottom example (yours), the phenyl is attached to a "one carbon" chain. therefore, propane is the main chain.