There's only one adjustment screw on mine, then a balancer(?) bar that connects to both cables. When you pull up the lever & when you let it down, both cables should move. If not, then you gotta find (& fix) whatever's sticking.

When the handbrake lever is down, both of the levers (back on the calipers) should be pretty much released out to their stops. You gotta look at how those levers work...

If those levers or the cables are sticky, the return springs might not be strong enough to release the calipers. If that's what's going on, tightening the cable adjustment will only muck it up even further...