It's called Orthostatic Hypotension. Normally, when you rise from a seated, squatted or prone position your blood vessels constrict to adjust for the change in resistance caused by gravity. If they didn't then as soon as you stood up all of your blood would pool to your feet and you would pass out. That is what you are experiencing except on a smaller scale. The good news is that this is likely to be a temporary side effect of positive changes occurring within your body due to your diet such as your insulin levels coming down, hence less sodium being retained by the kidneys (many people don't realize that insulin causes sodium retention) which along with lower blood sugar decreases blood volume, and less sympathetic tone (less adrenaline). It's a pretty common phenomenon when people start low-carb diets. Eventually you will adjust but in the meantime you need to make a conscious effort to stay well-hydrated, consume some sea-salt every day even if you don't want to, and remember to rise from a seated, squatted or prone position slowly so your body has more time to adjust to the drop in blood pressure.
While it is always possible, I think it is unlikely that you would simultaneously develop some other hypotensive disorder just after starting paleo or primal type eating. It's just too much of a coincidence.
You didn't mention if you are taking any blood pressure medications or diuretics. If you are then you will need to have the dosage decreased or possibly have the medication eliminated from your regimen altogether.
If the dizziness hits you and you feel like you are going to black out then you should of course sit down if possible. If you are game and want a more proactive approach then you can also try (at your own risk) bearing down like you were lifting a heavy weight (Valsalva Maneuver) which will increase your intrathoracic pressure, elicit a little epinephrine increasing your cardiac output and help pump more blood back up to your brain. It is similar to what fighter pilots do in heavy Gs to keep themselves from blacking out. Don't hold it very long (more than a couple of seconds) or it could have the opposite effect and make you pass out.