Files with solution for problem in StackOverflow question 25246280 (http://stackoverflow.com/q/25246280)

App1_MainPage.xaml

<Page
    x:Class="StackOverflow_25246280_App1.MainPage"
    xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
    xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
    xmlns:local="using:StackOverflow_25246280_App1"
    xmlns:d="http://schemas.microsoft.com/expression/blend/2008"
    xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006"
    mc:Ignorable="d">

    <Grid Background="{ThemeResource ApplicationPageBackgroundThemeBrush}">
        <Grid.RowDefinitions>
            <RowDefinition Height="100"/>
            <RowDefinition Height="*"/>
        </Grid.RowDefinitions>
        <Button Name="btnStart" Content="Start (app 1)" FontSize="30" Margin="10"
                HorizontalAlignment="Stretch" VerticalAlignment="Stretch"
                Click="btnStart_Click" />
        <TextBox AcceptsReturn="True" Name="txtDebug" Margin="10" Grid.Row="1" />
    </Grid>
</Page>

App1_MainPage.xaml.cs

using System;
using Microsoft.WindowsAzure.MobileServices;
using SO_25246280_Portable;
using Windows.UI.Xaml;
using Windows.UI.Xaml.Controls;

// The Blank Page item template is documented at http://go.microsoft.com/fwlink/?LinkId=234238

namespace StackOverflow_25246280_App1
{
    /// <summary>
    /// An empty page that can be used on its own or navigated to within a Frame.
    /// </summary>
    public sealed partial class MainPage : Page
    {
        public MainPage()
        {
            this.InitializeComponent();
        }

        private async void btnStart_Click(object sender, RoutedEventArgs e)
        {
            try
            {
                var client = new MobileServiceClient(
                    "https://SERVICE_NAME_HERE.azure-mobile.net/",
                    "SERVICE_KEY_HERE",
                    new AppSpecificTableNamesHandler("App1")
                );

                var table = client.GetTable<MyType>();
                var item = new MyType { Name = "John Doe", Age = 33 };
                await table.InsertAsync(item);
                AddToDebug("Inserted item with id = {0}", item.Id);

                item.Age = item.Age + 1;
                await table.UpdateAsync(item);
                AddToDebug("Updated item, age now = {0}", item.Age);
            }
            catch (Exception ex)
            {
                AddToDebug("Error: {0}", ex);
            }
        }

        void AddToDebug(string text, params object[] args)
        {
            if (args != null && args.Length > 0) text = string.Format(text, args);
            this.txtDebug.Text = this.txtDebug.Text + text + Environment.NewLine;
        }
    }
}

App2_MainPage.xaml

<Page
    x:Class="StackOverflow_25246280_App2.MainPage"
    xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
    xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
    xmlns:local="using:StackOverflow_25246280_App2"
    xmlns:d="http://schemas.microsoft.com/expression/blend/2008"
    xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006"
    mc:Ignorable="d">

    <Grid Background="{ThemeResource ApplicationPageBackgroundThemeBrush}">
        <Grid.RowDefinitions>
            <RowDefinition Height="100"/>
            <RowDefinition Height="*"/>
        </Grid.RowDefinitions>
        <Button Name="btnStart" Content="Start (app 2)" FontSize="30" Margin="10"
                HorizontalAlignment="Stretch" VerticalAlignment="Stretch"
                Click="btnStart_Click" />
        <TextBox AcceptsReturn="True" Name="txtDebug" Margin="10" Grid.Row="1" />
    </Grid>
</Page>

App2_MainPage.xaml.cs

using System;
using Microsoft.WindowsAzure.MobileServices;
using SO_25246280_Portable;
using Windows.UI.Xaml;
using Windows.UI.Xaml.Controls;

// The Blank Page item template is documented at http://go.microsoft.com/fwlink/?LinkId=234238

namespace StackOverflow_25246280_App2
{
    /// <summary>
    /// An empty page that can be used on its own or navigated to within a Frame.
    /// </summary>
    public sealed partial class MainPage : Page
    {
        public MainPage()
        {
            this.InitializeComponent();
        }

        private async void btnStart_Click(object sender, RoutedEventArgs e)
        {
            try
            {
                var client = new MobileServiceClient(
                    "https://SERVICE_NAME_HERE.azure-mobile.net/",
                    "SERVICE_KEY_HERE",
                    new AppSpecificTableNamesHandler("App2")
                );

                var table = client.GetTable<MyType>();
                var item = new MyType { Name = "John Doe", Age = 33 };
                await table.InsertAsync(item);
                AddToDebug("Inserted item with id = {0}", item.Id);

                item.Age = item.Age + 1;
                await table.UpdateAsync(item);
                AddToDebug("Updated item, age now = {0}", item.Age);
            }
            catch (Exception ex)
            {
                AddToDebug("Error: {0}", ex);
            }
        }

        void AddToDebug(string text, params object[] args)
        {
            if (args != null && args.Length > 0) text = string.Format(text, args);
            this.txtDebug.Text = this.txtDebug.Text + text + Environment.NewLine;
        }
    }
}

Portable_AppSpecificTableNamesHandler.cs

using System;
using System.Net.Http;
using System.Threading;
using System.Threading.Tasks;

namespace SO_25246280_Portable
{
    public class AppSpecificTableNamesHandler : DelegatingHandler
    {
        public const string TablePrefix = "MyType";
        private const string TablesPathPrefix = "/tables/";

        private string tableSuffix;
        public AppSpecificTableNamesHandler(string tableSuffix)
        {
            this.tableSuffix = tableSuffix;
        }

        protected override Task<HttpResponseMessage> SendAsync(HttpRequestMessage request, CancellationToken cancellationToken)
        {
            UriBuilder uriBuilder = new UriBuilder(request.RequestUri);
            string path = uriBuilder.Path;
            if (path.StartsWith(TablesPathPrefix + TablePrefix))
            {
                path = TablesPathPrefix + TablePrefix +
                    this.tableSuffix + path.Substring(TablesPathPrefix.Length + TablePrefix.Length);
                uriBuilder.Path = path;
                request.RequestUri = uriBuilder.Uri;
            }

            return base.SendAsync(request, cancellationToken);
        }
    }
}

Portable_MyType.cs

using Microsoft.WindowsAzure.MobileServices;
using Newtonsoft.Json;

namespace SO_25246280_Portable
{
    [DataTable(AppSpecificTableNamesHandler.TablePrefix)]
    public class MyType
    {
        [JsonProperty("id")]
        public string Id { get; set; }

        [JsonProperty("name")]
        public string Name { get; set; }

        [JsonProperty("age")]
        public int Age { get; set; }
    }
}