It is a fairly simple system, but it needs to be adjusted properly and that is something you can do. Better on a windless day when you can hoist the sail and drop it.
The control lines must be vertical and should be attached mechanically to the topping lift. If the lines are not vertical the sail will not raise or drop freely.
The topping lift must be tight when you drop or raise the sail. You may even want to do this with the boom raised a bit at the clew so that you are not pulling the leech when you raise the sail.
Once you sort out the vertical attachment points on the topping lift, mark it so that you can set it there for hoisting and lowering the sail. This will insure that the control lines are always vertical for the hoist or drop.
When the sail is flaked it should properly sort out on alternate sides of the boom and develop memory when dropping.
You might want to consider an "extension" to your topping lift which has the control lines attached to it and this extension is hoisted by your topping lift. This allows you to keep the integrity of the topping lift and maintain the position of the control lines when you remove the sail.
There are usually small plastic clamping devices which become a stop on the control line so they can move up a bit but not down. Unscrew them or untwist whatever you need to do to get the control lines fair, vertical and taut or equally tensioned. The sail needs them taught to be guided up and down.
When sailing release the topping lift tension.
When dropping the sail bring the boom to CL ease the mainsheet and tension the topping lift and release the halyard. The sail should easily drop and flake itself. A bit of wind helps, but sometimes depending on the weight of the sail, and the number of reefing lines and so forth you might have to give a tug at the mast or on the leech. Make sure your main halyard can run free when dropping.