I disagree this is an aerator problem. Aerators do nothing to retain or drain water in the spout, it is geometry and gravity. A clogged aerator will extend the time it takes to fill an empty spout, but will also severely restrict water flow to a noticeable degree. By all means clean the aerator, most of them could use some cleaning.
The spout should retain water regardless of aerator condition. Even if it were empty, unless the valve is opened very slowly, it will fill extremely quickly and water flow will be seen in much less than 1 full second.
The problem could be in the valve assembly, but the linkage would need to be such that the valve opening speed is not directly related to the lever operation speed, which would be an unusual configuration.
Another cause could be the water supply is saturated with air or some other gas. When the water sits, the gas separates from the water and causes a sizable bubble to build in the pipe just below the valve. It will take a bit of time to push this gas out of the pipe before water flow is observed. Depending on pipe configurations, this may or may not be observed at other faucets.
When gas or air collects this way, the little bit of water in the spout is usually expulsed rather violently, as compressed air flows much faster than water under pressure. This is typically rather startling to the person using the faucet. If this behavior is not observed, this is unlikely the explanation.