I run an Umbraco 7 site as a Azure WebSite where I try to stay up to date with modern approaches like git updates and nuget package installation.
I had a site setup with Nuget Install-Package UmbracoCms for version 7.1.3. The site has version control with git, gitignoring packages and bins. Now when I needed to upgrade to 7.1.4 my successful process was:
Update-Package UmbracoCms (http://our.umbraco.org/documentation/Installation/Upgrading/general)
Then git commit and push to get the info to my VSO repository.
And in the Visual Studio Online (Monaco) console I needed to restore the packages and re-build manually:
nuget restore mysolution.sln