Yes, the wastegate pressure determines the minimum pressure you can hold.
The reasons may not be quite so obvious, and there are several factors that could cause a "12 PSI wastegate actuator" to actually only deliver 10PSI.
First, you have to picture the forces going on here. If you have a simple internal wastegate actuator with a single port You basically have a diaphragm that the boost pressure can act against, on the other side of the diaphragm is a spring that gets compressed as the boost pushes the diaphragm down and a rod that moves with the diaphragm and opens the wastegate itself. So Boost Pressure->Pushes on Diaphragm->Compresses spring->Opens wastegate.
With a boost controller in there you're basically intercepting the boost pressure input to the actuator and either blocking it entirely or bleeding some of it off (different boost controllers work slightly differently). This allows you to make, say, 20PSI on a 10PSI wastegate. The EBC simply blocks/bleeds the boost reference until it approaches 20PSI, then it lets it all through. Since 20PSI is more than enough to compress the spring in your 10PSI actuator, it opens reducing turbine speed and therefore holding boost at 20PSI.
However, boost pressure isn't the only pressure acting on the spring. It also has to hold the wastegate closed against the exhaust backpressure in the manifold. This backpressure is always trying to force the wastegate open and only the spring is able to keep it shut.
This is why some cars that are able to hold a steady 10PSI (or whatever) of boost suddenly see boost creeping up to 12-13PSI when they install a free flowing exhaust manifold, exhaust system, big cams, whatever. There's now less exhaust backpressure trying to open the wastegate so it takes more boost to do it. This is also why simple 1-port wastegate actuators don't work well when trying to run really high boost on a light spring. If your wastegate actuator spring is meant to run 10PSI and you install a boost controller and try to make 30 PSI (don't do this, BTW
) then it will likely fail to hit that boost since the exhaust backpressure alone is enough to open the gate. This is why dual-port wastegates/actuators exist.. but that's an entirely different discussion.
Another reason a turbo might only make 10PSI on a 12PSI actuator is that the engine might be out-flowing the turbo. This is not what is happening to you as it normally only happens when using too small of a turbo for the power goals. You can go down a huge rabbit hole of discussing compressor and turbine flow maps, surge lines, etc... but suffice it to say, your actuator is probably just going to make 10PSI on your car and everything is just fine. Upgrade your exhaust
-Matt