Just put it here. I found out that if we didn't redirect to the route that return inertia response. It'll throw us to the default route.

Here is my setup

File: app/Providers/FortifyServiceProvider.php

use Laravel\Fortify\Contracts\LoginResponse as LoginResponseContract;
use App\Http\Responses\LoginResponse;

/**
     * Register any application services.
     */
    public function register(): void
    {
       // Register LoginResponse as a singleton to prevent any binding 
        $this->app->singleton(LoginResponseContract::class, LoginResponse::class);
    }

File: app/Http/Responses/LoginResponse.php

class LoginResponse implements LoginResponseContract
{
    public function toResponse($request)
    {
        $user = $request->user();

        if ($user->isCustomer()) return redirect()->route('customer.index');
        return edirect()->route('admin.index');
    }
}

File: app/Http/Controllers/CustomerController.php

public function index()
{
    return Inertia::render('customer/index');
}

and the route file.

Route::get('/admin, function () {
    // This controller or route must return as an Inertia response  
    return Inertia::render('admin/index');
})->name('admin.index');

Route::get('customer', [CustomerController::class, 'index'])->name('customer.index'); 

That's all, I hope it help.

May I ask the question? So you return the Inertia render page instead of the redirect anymore, right?