Swinging bird nest

We were gifted a wicker hanging bird nest and I put it in the only available place in our garden. It’s been over a year and I had never seen anything near it until tonight when I saw a little head poking out. I was so excited but I’ve come home this evening and it’s so windy, the nest is swinging all over. I’m sure if they’re not happy or safe in there they will just fly off but my question is, is it worth trying to secure it so they don’t get hurt, or should I wait until I’m sure it’s unoccupied and secure it for future birdies??