Shilpa,
From the FAQ at crosswordlabs:
I filled in the crossword and now everyone can see what I typed in!!!
Only someone using your computer and web browser can see what you typed in. No one else can. CrosswordLabs saves your responses in your web browser's storage system. This ensures if you refresh the page or close the browser accidentally, you don't lose all your responses. People on other computers or different browser contexts won't see your answers.
The only way a person can see another person’s work is if they use the same account on the same computer. If they do, then yes, they will see the partially completed puzzle. Otherwise, no.