I just recently replaced the clutch on my 2007 Subaru Impreza. I did the clutch myself and had the flywheel resurfaced at a shop. The car shakes when i accelerate from park to first until I release off the clutch completely. The clutch is also a stage 3 Exedy.
Looking on Exedy's website, I don't see a specific listing for a "Stage 3" clutch from them, but typically, higher stage clutches will have some amount of chitter no matter the manufacturer. This usually has to do with the type of materials used so the clutch will have more bite (or grip), and thus more holding power while engaged. These usually use "exotic" materials such as carbon fiber or Kevlar. What you are experiencing is probably completely normal.
Secondarily, something else to think about is bedding the clutch (or the break-in period). Most clutch manufacturers have a break-in period for their clutch in which they don't want you to use it too severely during the process. With high performance clutches I've installed in the past, I believe the manufacturer wanted the first 500 miles of usage (stop and go miles, not highway) to be taken easy so the clutch would break in correctly. During this period you'll notice a higher degree of bite while slipping the clutch. Once it gets fully broke in, the chitter you are experiencing might lessen. This is just what happens naturally.
From Exedy's FAQ page (#10 Under Stage 1/2):
The Stage 1 Organic kits will drive similar to the OEM clutch but will have an increased pedal effort. The Stage 2 Cerametallic clutch will have a more aggressive engagement and take off RPM may need to be increased for a smoother take off.
If a "Stage 3" is even more aggressive, you'd more than like be experiencing chitter during engagement.