Shell redirection doesn't move file position for stdout

Question

I have a minimal complete example where the Linux API behavior seems to be a bit ambiguous. The stdout is closed, reopened and used as a regular file's descriptor:

#include <stdio.h>
#include <stdlib.h>
#include <fcntl.h>
#include <unistd.h>

int main(void) {
     system("echo > testfile");
     fclose(stdout);
     int fd = open("testfile", O_WRONLY);
     if (fd < 0) {
          perror("open():");
          return -1;
     }

     dprintf(fd, "Test\n");
     system("echo Test2");
     system("echo TestFFFFFFFFFFFF >> /proc/$$/fd/1"); // problem line
     sleep(5);
     dprintf(fd, "Test4\n");
     system("echo Test5");

     return 0;
}

Before sleep in testfile I see

Test
Test2
TestFFFFFFFFFFFF

But after sleep this line is overwritten:

Test
Test2
Test4
Test5
FFFF

It seems that for regular files this behavior is strange: if we write something to file - we change its position an appropriate way (to the end).
But for stdout it looks quite reasonable: if we write to stdout - we rewind its position back after finish writing (to the start).
Is this a bug or the right way?

P.S. Besides the bash I also tried dash and ksh - the same thing.