Most springs do need to be oiled to help reduce the crunching or squeaking noise that most springs tend to make when they are stretched and compressed. However, some cheaply made springs will still make noise even when oiled.
Those springs made from alloy materials, which are found in some of the more expensive springs, tend to be quieter.
You may also get some noise from the frame if it twists or shifts while you are rebounding. This is usually from cheaper frames or from frames that don't fold at all.
We didn't have too much trouble with this when trying the ones we've featured on our list although there is, naturally, some noise is to be expected.