There is no way to capture the time that a ticker symbol is added to a dynamic watchlist (which has it’s content automatically updated by a saved custom scan). I will also note that for a dynamic watchlist, the list of ticker symbols should always reflect the current results output of the scan. If you are using a 5 min time frame, the only symbols in your dynamic watchlist should be from the last 4 min 59 seconds. Any ticker symbols from a previous 5 min bar should be wiped away.
So given this, what is the value in trying to acquire the time in which any one of those ticker symbols were added? At any given time everything in the watchlist represents the current results output of the scan.
You may say that you are using a daily time frame for the scan, or even an hourly. In this case you may end up with ticker symbols that were added at any point during that time span. So using a daily time frame you may end up at the end of the day with ticker symbols that satisfied the scan criteria in the first hour of trade. There is no way to capture that data.
If this scenario aligns with your current setup, there is only way I know of to keep track of what time of day any given symbol was picked up by the scan. (apart from reviewing the list of messages in the alert menu). They only other way is to create a dynamic alert from that saved scan. Set the alert to send you emails. Then you will have the time stamps in your inbox. Although clumsy, this is the only option available.