Suggestion for cracked stairs

We are first time home owners and complete noobs at DIY. We had a carpet runner installed on our wooden steps and the fitter caused the cracks on the bottom step as seen in the photo. He told us to simply fill it up with polyfilla. There were hairline cracks in other steps too, but those look benign compared to this one. Should we be more worried about this. I wanted to take suggestions from the community on the best way to fix/patch it up. Any help appreciated, thanks.