Yes, that is correct. Especially, if you didn’t submit it online, but send it by letter post.
If you used ZHprivateTax, make your amendments, print it out, sign it and send it incl. all supporting documents (like you did first time). I also suggest to make additional notes on a separate A4 explaining that you are submitting the adjusted tax declaration and what exactly you amended.
If you submitted the tax return online, then the procedure is a bit complicated. But as I understand, it’s not your case.
Best regards, Pope