The integration plugin is intended to more-or-less reproduce the standard theme design rather than be an exact copy, and the alignment of the menu appears to have been over-looked.
It can be easily remedied by adding the following CSS rule to Toolset > Layouts CSS & JS:
There seems to be somewhat other minor differences in css as well - ie: the integrated layouts (pages) seem to have a bit more padding all around.
It would be very useful if there was list of these small differences with our integration themes so that we can remedy them all at once using the css..
Themes such as twentysixteen are typically the starting point for people's projects, rarely the end, and developers would customarily make modifications to the CSS to personalise the design.
That is why the objective of the Toolset integration plugins is not to replicate pixel-by-pixel the existing design, as the expectation is that users will want to customise the design in any case.
If there were any areas where the markup was such that it made it difficult or impossible to use CSS to recreate a particular look then the team responsible would have to address that, but hopefully tweaks to the CSS will be all that is required to achieve a specific layout.
If there is an element of the design you find you are having problems modifying then please let me know and I'll be happy to help.