The white circle appears exactly on the onset (start) of the parent event. Thus, you can add a proxy variable to 'Onset Time' of the event and then record a value into Data Report (e.g. with Reporter element)
Registering Triggering Time is similar- create a proxy variable for the 'Triggering Time' property of the Button element and save it into Data Report after a response if given.
For both variables, it is best to save them after the event with circle, when the variables contain new values. Note the Onset Time returns a global timestamp (ms since the start of the experiment, while Triggering Time returns a local timestamp (ms since the event onset)