With the newer Umbraco versions you would have to override authentication methods in OWIN to execute custom code on login and signout. For my project I had to do something similar. The code sample below will probably help you. I don't have a sample for the logout part but this will probably guide you in the right direction.

public class Startup : UmbracoDefaultOwinStartup
{
    protected override void ConfigureUmbracoUserManager(IAppBuilder app)
    {
        app.ConfigureUserManagerForUmbracoBackOffice<BackOfficeUserManager, BackOfficeIdentityUser>(
            ApplicationContext,
            (options, context) =>
            {
                var membershipProvider = MembershipProviderExtensions.GetUsersMembershipProvider().AsUmbracoMembershipProvider();
                var settingContent = UmbracoConfig.For.UmbracoSettings().Content;

                var userManager = BackOfficeUserManager.Create(options,
                    ApplicationContext.Current.Services.UserService,
                    ApplicationContext.Current.Services.EntityService,
                    ApplicationContext.Current.Services.ExternalLoginService,
                    membershipProvider,
                    settingContent);

                userManager.BackOfficeUserPasswordChecker = new CustomBackofficePasswordChecker();


                return userManager;
            });
    }
}

public class CustomBackofficePasswordChecker : IBackOfficeUserPasswordChecker
{
    public async Task<BackOfficeUserPasswordCheckerResult> CheckPasswordAsync(BackOfficeIdentityUser user, string password)
    {
        //Execute custom code

        return BackOfficeUserPasswordCheckerResult.FallbackToDefaultChecker;
    }
}