I have never ridden a horse in side reins for schooling, but I usually lunge in side reins so that the horses have a contact to work into. When they are going forwards nicely and working through from behind, there needs to be some sort of contact at the front end to control the energy that's being created by the back end - otherwise the energy is lost through the front and you find that the horse rushes and / or falls onto the forehand.
I use stretchy rubber side reins, running directly from the bit (eggbutt snaffle) to a roller. From the saddle the aim is to have the horse's head more or less on the vertical, so I want the same when they're working on the lunge. The aim is to encourage the horse to carry its head on the vertical and work into the contact, but not to force anything. With ridden work I want to have giving hands and an elastic contact that encourage correct head carriage by pressure and release. I try to replicate this in some way whilst lunging.
I set the side reins long enough that there's only a light contact when the horse is on the vertical, and short enough that when they go above the vertical the pressure increases. When they feel the contact strengthen they lower their head to escape that pressure, and as they do this the pressure eases off again. This is why I prefer to use the stretchy rubber ones - the horse does have the ability to resist them, and because they expand and contract according to the amount of resistance, they are closer to replicating the elastic contact that you are aiming to have from the saddle. As I'm lunging it's clearly visible when the horse is resisting the contact and when they are accepting it.
Everybody has their own way of using side reins. Mostly it depends on what you're doing and what you're hoping to achieve. As with any training aid, they do have their place if used correctly.