Timeout in select does not work after non blocking connect function call

Question

I'm writing a "hello world" client application which has a non-blocking connect function call. I have an echo server which is listening 3000 port on the same host and I want to implement connect mechanism with 10 second time out. I have set the client_fd socket to non-blocking mode. After connect execution function I call select with needed timeout, but the next line of code (printf("Writing it immediately after select\n");) executed immediately.

#include <stdio.h>
#include <errno.h>
#include <stdlib.h>
#include <sys/types.h> 
#include <sys/socket.h>
#include <arpa/inet.h>
#include <unistd.h>
#include <fcntl.h>
#include <sys/select.h>
#include <sys/time.h>

int main(void)
{
    int error;
    socklen_t len;
    fd_set rset, wset;

    // Creating socket
    int client_fd = socket(AF_INET, SOCK_STREAM, 0);
    if (client_fd < 0)
    {
        perror("[Socket creating] ");
        return -1;
    }

    // Setting socket in non-blocking mode
    int flags;
    flags = fcntl(client_fd, F_GETFL, 0);
    if (fcntl(client_fd, F_SETFL, flags | O_NONBLOCK) < 0)
    {
        perror("[Setting socket flags]");
    }

    struct sockaddr_in addr;
    addr.sin_family = AF_INET;
    addr.sin_port = htons(3000);
    addr.sin_addr.s_addr = inet_addr("127.0.0.1");
    int n;
    n = connect(client_fd, (struct sockaddr*)&addr, sizeof(struct sockaddr_in));
    if (n < 0)
    {
        if (errno != EINPROGRESS)
        {
            return -1;
        }
        else
        {
            printf("Connection in progress!\n");
            FD_ZERO(&rset);
            FD_SET(client_fd, &rset);
            struct timeval tval;
            tval.tv_sec = 10;
            tval.tv_usec = 0;
            int ret = select(client_fd + 1, &rset, NULL, NULL, &tval);
            printf("Writing it immediately after select\n");
            printf("ret: %d\n", ret);
            perror("[select error]");
        }
    }
    else if (n == 0)
    {
        printf("Connection has been completed!\n");
    }
    else
    {
        printf("Waiting connection!\n");
    }

    close(client_fd);
    return 0;
}

When the echo server is not running and I run client I have the following situation:

$ ./client 
Connection in progress!
Writing it immidiatetly after select!
ret: 1
[select error]: Operation now in progress

What I do wrong here? Is it a right way to implement non-blocking connection with some timeout?