The willows they're referring to are the willows (and dogwoods) that are grown for the vibrant colours of their new growth. You cut them right back every year at the end of winter, then they grow long stright whippy shoots in the spring/summer and when the leaves fall in the autumn you're left with vibrant red/yellow/acid green stems which look fantastic in the clear winter sunshine 
You're growing a twisted willow which is grown for its wonderful form. If you've got room to let this grow big you can leave it - it will grow into a tree with twisted corkscrew branches that will look fabulous in the winter.
If you only have a small garden you can cut it back at this time each year and it will grow back every year. You can use the twisted twigs that you cut off for flower arrangements etc.
Or if you want to you can leave it as it is for a few years then cut it back (at this time of year) when it is outgrowing its space.
Don't worry, you won't kill it - and if you want to you can stick the prunings in the ground and they will all grow and you can dig them up, pot them on and give them to friends