Welcome ferney. Any thing you plant in this yard this year will be in jeopardy from the soil sterilant used. To clear the soil would mean either removing it and replacing, which is a huge job and can be expensive. Waiting and watering regularly to wash away the Scott's poison is the best way. The mulch will not harm your soil at all. It is very good for it and will help put back in some of the nutrients that were killed off.
Good luck!