If you’re not using the right mix of composting materials (carbon-nitrogen ratio, and nothing in there which shouldn’t be), it won’t work well, and neither will other methods.
As you’d always be adding new material, you’re never going to get to fully finished compost – that is, part of what’s in the can will get there, but other parts won’t be, and I don’t see how that method’s going to let you separate them. Are you sure you didn’t misunderstand instructions telling you to fill one can, then leave that one while you fill the other, then use the contents of the first one and start over? Or to have two sets of cans, with the weekly dumping being meant to substitute for turning the pile?
Whether you need to add water depends on how wet it is; which is going to depend both on the moisture content of what you put in the can, and the outside humidity (and, if you don’t have the lid on, whether it rains.)
There’s also the question of what you’re aiming for. Aiming for something that got hot enough for long enough to kill pathogens, aiming for something that won’t stink too much until you can till it into your garden, and aiming for something you can use in a potting soil mix aren’t the same thing.