Question about packing liquids

If I have bottles of Soap and Glory cleansing lotion with a pump action dispenser on top that can be twisted to open or shut to determine whether the lotion can be dispensed or not, is this classed as double-sealed. The documentation mentions double sealed liquid containers as having a separate piece of plastic around the lid that needs to be removed, eg, like you'd find on most bottles of water, or foil removable covers under the lid, like you might find on a bottle of milk or tube of toothpaste. However, I can't find anything about pump-action lids. Could anybody advise please? Thanks