what does the timer signify in the name/activity column?

If you are referring to the (18min) or (*) that appears beside someones planet name in the galaxy menu, it is the last reported activity, (*) means it happened not long ago (I think the timer starts at 15min after last reported activity). Activity could be an attack or espionage on the planet, something one the planet finishing construction, ect.

are you sure finished construction activates a timer? i hav'nt seen that myself
what does etc mean? as far as i know timer appears when someone is esp'd, attacked or logged in while in vmode

i would like to know exactly what sets off the timer as well