If your cleaner feels sudsy during the cleaning step, then it should be absolutely free of that feeling after rinsing. You want your lens to be absolutely free of the cleanser, as if you were about to put it in your eye. But don't put it into your eye, because while you've cleaned your lens, you're not done. Just because you placed your lenses into their case doesn't mean you are actually disinfecting them. Be sure and follow the solution's manufacturer's directions.
Different solutions require different lengths of time.
Just like before, rinse them according to manufacturers directions. If you keep them for a week or more, consider removing these deposits once a week. Your lenses will be cleaner, since the daily solutions can reach them more easily. They'll also be more comfortable and clearer. Again, follow the manufacturer's directions.