Some machines do that, others don't. I found my vintage machines are better at pulling the fabric in straight. But then, my 1924 Singer was really pulling the bottom fabric to the right.
If you don't have a stiletto, skip that, you do have a stiletto. Any small dowel will work. I use chopsticks from restaurants. Put it into your pencil sharpener very gently until it has a point as sharp as you like. Not quite sharp to the end is better.
Hold that seam end with the stiletto until the very last thread has exited the needle.