We all know when these triggers go off, but things can get confusing when multiple effects are triggered all at once. To be clear, Counters go off the moment your HP go from a higher number to a lower number as a result of an action, as long as that lower number is greater than 0. Close skills go off the moment your HP go from a higher number to a lower number as a result of an action, as long as that higher number is greater than 0, and the lower number is 0 or less.
This means that when a single set of actions are resolving in a chain, if your unit has both a close and a counter skill, and is hit 10 times, then your counter will go off each time you are hit, except the time that puts you at 0 or below, and every time after that. The hit that puts you at 0 or below will trigger your close skill, and no others will.