The EF code first tooling (> EF 6.X ) works very well and supports your use-case out-of-the-box to allow developers to follow best-practices by separating DB/EF from Web context/projects. It is really a matter of understanding the tools and of doing things in the right way. I would recommend you setup a fresh solution to just try code-first migrations. If you do not get this working in an isolated way, do not throw away your time while testing over and over again in your real project/solution.
While settings up code-first migrations in our project my team was supported by Microsoft employees. They just did it right and we saved some bits in our documentation.
While browsing the Internet I found these pages helpful, I know there is plenty of help to deal with EF code-first development and deployment (especially using Visual studio deployment to Azure App service).
Since your question is rather difficult to answer, I would recommend you follow best-practices and documentation written for EF 6.X and VS2015 and come back to SO with a better understanding of tools you need to solve your problem. Then either edit your question or just ask another ones.
To give you some appetizers just look at the help of migrate.exe - a tool to run code-first migration from commandline. There is everything you probably need.
migrate.exe
Code First Migrations Command Line Utility
Applies any pending migrations to the database.
migrate assembly [configurationType] [contextAssembly] [/targetMigration]
[/startUpDirectory] [/startUpConfigurationFile]
[/startUpDataDirectory] [/connectionStringName]
[/connectionString] [/connectionProviderName] [/force] [/verbose]
[/?]
assembly Specifies the name of the assembly that
contains the migrations configuration type.
[configurationType] Specifies the name of the migrations
configuration type. If omitted, Code First
Migrations will attempt to locate a single
migrations configuration type in the specified
assembly.
[contextAssembly] Specifies the name of the assembly that
contains the DbContext type if different from
the assembly that contains the migrations
configuration type.
[/?] Display this help message.
[/connectionProviderName] Specifies the provider invariant name of the
connection string.
[/connectionString] Specifies the connection string to use. If
omitted, the context's default connection will
be used.
[/connectionStringName] Specifies the name of the connection string to
use from the specified configuration file. If
omitted, the context's default connection will
be used.
[/force] Indicates that automatic migrations which might
incur data loss should be allowed.
[/startUpConfigurationFile] Specifies the Web.config or App.config file of
your application.
[/startUpDataDirectory] Specifies the directory to use when resolving
connection strings containing the
|DataDirectory| substitution string.
[/startUpDirectory] Specifies the working directory of your
application.
[/targetMigration] Specifies the name of a particular migration to
update the database to. If omitted, the current
model will be used.
[/verbose] Indicates that the executing SQL and additional
diagnostic information should be output to the console window
According what configuration parameters you pass to the migration tooling you either run an explicit, a configuration-file based or a convention-based migration. Pay close attention to what migrate is printing as output of Origin
1. Explicit parameters
migrate.exe "Fireframework.Web.dll" "Fireframework.Web.Migrations.Configuration" /connectionString="Data Source=tcp:fireframeworkdbs.database.windows.net,1433;Initial Catalog=fireframeworkdbdev;User Id=ffdbadmin@fireframeworkdbs;Password="secret" /connectionProviderName="System.Data.SqlClient" /verbose
2016-04-25T08:06:09.9183260Z VERBOSE: Target database is: 'fireframeworkdbdev' (DataSource: tcp:fireframeworkdbs.database.windows.net,1433, Provider: System.Data.SqlClient, **Origin: Explicit**).
2016-04-25T08:06:13.5640428Z No pending explicit migrations.
2. By Configuration file
migrate.exe "Fireframework.Web.dll" "Fireframework.Web.Migrations.Configuration" /startUpConfigurationFile="web.config" /verbose
VERBOSE: Target database is: 'fireframework' (DataSource: (LocalDb)\MSSQLLocalDB, Provider: System.Data.SqlClient, **Origin: Configuration**).
Applying explicit migrations: [201603161334138_InitialCreate, 201604081002396_Add_Simulation_CreatedDateTime_Property, 201604201138442_Add_Simulation_AbortRequestPending_Property, 201604211315107_Rename_Simulation_Properties].
Applying explicit migration: 201603161334138_InitialCreate.
3. By Convention
migrate.exe "Fireframework.Web.dll" "Fireframework.Web.Migrations.Configuration"
VERBOSE: Target database is: 'Fireframework.Model.DatabaseContext' (DataSource: .\SQLEXPRESS, Provider: System.Data.SqlClient, **Origin: Convention**).