How To Identify If SharePoint App is installed on On-Premise or In Cloud?

This can be determined by Context Token as follows

protected void Page_Load(object sender, EventArgs e)
{
  Uri hostWeb = new Uri(Request.QueryString["SPHostUrl"]);
  string contextTokenString =
    TokenHelper.GetContextTokenFromRequest(Request);

  if (string.IsNullOrEmpty(contextTokenString))
  {
    // if On-Prem
    using (var clientContext = TokenHelper.GetS2SClientContextWithWindowsIdentity(
      hostWeb,
      Request.LogonUserIdentity))
    {
      . . .
    }
  }
  else
  {
    // if Office365
    using (var clientContext = TokenHelper.GetClientContextWithContextToken(
      hostWeb.ToString(),
      contextTokenString,
      Request.Url.Authority))
    {
      . . .
    }
  }

  . . .
}

Read further to understand hybrid authentication 

Thank you Tsuyoshi Matsuzaki