I've had the exact same issue several times - not always caused by Resilio. Most times the advice I am about to give fixes it - once I had to factory reset the NAS and start over - a painful experience.
In the NAS web UI - Go to the Shares tab and then repeat the following steps on each affected share.
1. Mouse over the share to view the cog symbol, click the cog and select Settings from the dropdown
2. Select the File Access tab at the top and then RESET from the left hand menu
3. Reset Permissions
With any luck you will gain full control of your files.
