Some fish are more skittish than others, but it's obvious he's bothered by the sudden "lights out." I see a couple solutions to this issue.
1. Buy another clown. Having a companion may settle him down considerably, or at least distract him and make him less nervous.
2. If there's any way to cover the filter, do so.
3. Contrary to popular belief, clownfish host anemones (not the other way around.) Nem's need strong lighting, good conditions and good water flow. They can be quite picky, believe me. If you're prepared for it, by all means, go ahead. Or, you could pick a different coral to host your clown. Pulsing xenia torch coral work the best I've found.
4. If you do choose the alternate coral option, be sure to keep your copperband well fed, lest he pick at your corals. Even being well fed, some butterflyfish will continue picking out of boredom sometimes :P
5. Switch up your lighting. There are timed lighting systems out there that mimic dawn and dusk, so as to limit stress on marine fish and create a more fluid/seamless/natural habitat.
6. Good luck with whatever option(s) you choose.