A neighbour of mine has an invisible fence and it does not stop their dog from running after foxes and deer.
I do allow my cats outside and feel that training them on their boundaries is very important. Do you have something to put on your side yard that you can put up to show them the boundary of the back yard so you can train them that they are only allowed out back? Training them may alleviate the fear of them getting free and not knowing the area
or where they are allowed.
I have trained my cats on a leash and harness and their boundaries. I live in a rural, wooded area with lots of temptations to run after wildlife. During training, I attached a harness with a long string attached and would not allow them to venture passed the mowed area of the lot (they are stopped dead when they try to venture farther). It did take a lot of patience and my time walking them, but has paid off for the most part. One will stop on command when I clap my hands and say "no" and the other is pretty good about stopping. Both these cats were trained as adults, not as kittens. The only thing is you need to have something that will show them the boundary. For me it is unmowed grass.
I do want to point out that they are NOT ALLOWED OUTSIDE WITHOUT 100% SUPERVISION.