How do you use a hot start timer?

Sorry if this is the wrong section, but I don't see an electrical section. My power goes off for a second at a time every now and then, which is causing my bulbs to hot start and fry them out. I'm using a battery powered back up timer, so they go right back on. Anyways, I was looking at these CAP 15 minute delay hot start timers, do they just plug into the side of my digital timer and that it? I don't know if they'll fit against the wall with the timer pressed into the outlet, and I don't want to spend $75 trying to figure it out. They don't look like they have any buttons on them, so I'm guessing this is how they are used? Any help would be great, I'm really tired of blowing money on new bulbs. Any other suggestions would be great, besides moving into a better location with better electrical, since that isn't an option at this time. Thanks

What kind of bulbs and how many watts? A backup battery for a computer would work if your setup is small enough. It wouldn't last very long, but it would definitely last a couple of seconds.