The swarm should be over in about an hour, but there's not much more you can do other then vacuum them up. It must of rained there recently.
There's nothing the bug man is going to do to remedy the problem, short term. The house needs to be properly treated. The chemicals pumped into the ground keeps them out and the bait stations will eventually kill the nest. I think Orkin does both, I don't know about Terminix. I think it varies with region. There are plenty of smaller firms that do the work. Who ever does it, they need to identify the installation issues of your particular house to make the treatment effective.
Ron

I suspect that they are not termites, as termites keep a low profile. At my previous house we would annually get a swarm of flying ants coming out of the wall about this time of year. While I am adverse to using pesticides, I would usually break out the can of Raid and whack them. For some reason they reappeared in the same place each year for a number of years. But, if you hit them with the spray you will take care of your problem, and they won't continue to swarm. This approach is much cheaper than getting an exterminator, and probably safer given the nasty toxics and liberal quantities they often use to eliminate a problem. Good luck.

The swarm took several hours - I simply sat with the vacuum hose and sucked them up as they came out. What bothers me is that this is an interior wall. We do have a contract with Orkin who treated the house and "checks" every year. They will not be able to be here to spot treat until next week. They recommended putting tape over the tiny area. Said that would confuse them and they'd die - then pull tape off, suck up the dead ones and apply new tape. (For this I spend $180.00 per year!) I don't want the chemicals in the house either but don't think I've got a choice here. I'm thinking my next battle will be wanting them to retreat the foundation because somehow they are getting in. I've gone over the exterior and there are no visable tubes - nor are there any in the house. I'm thinking they are coming in around the water pipes. Never changed the vacuum bag so many times in my life!

Any idea what product Orkin is using to treat the foundation?

This is the time of year termites swarm. It's easy to determine if they're termites or ants, just look at them and compare it to a picture if you're not sure.
The most susceptable areas for termite invasion are your doors into the house. The steps cover the entrance points and conceal the areas behind the stoops and they can get into the rim joists undetected. If the drill points are too far apart or don't get down into the dirt, the area is effectively untreated.
You need to examine any areas of the exterior where a structure is attached to the house that is as high or higher then the rim joist. Then go inside and open any ceilings that match up with the outside areas. You should see evidence at these points. Leave access holes in these areas so they can be checked regularly. You need to investigate and do inspections every year. The termite inspections are so limited in scope as to be useless.
If they are coming out of interior walls you may have substantial damage at the sill plates, rim joists and joist tail ends where they sit on the sill plate.
Ron

Thanks for the good info Ron. Tomorrow I'll be quite busy! I have checked around the foundation but will admit I didn't properly look upward. I haven't dug out my paperwork as to what product they've used in the past, again something on my to do list for tomorrow. The tape is keeping them in the wall, not coming out. I feel like I'll have a battle on my hands when they come - interior wall definitely means they've been eating something! My poor house! Thanks again.