I assume by "color correction" you mean color management. i.e., You have enabled a working space color profile for the project.
What you describe is likely normal behavior for After Effects. The factors here are the frame requirements (dimensions, frame rate, bit depth) and CPU speed. You can improve performance by reducing the resolution or frame rate of your preview, or by disabling View > Use Display Color Management. If your project is set to 16- or 32-bpc, reducing the color depth will also improve performance, of course at the cost of the color accuracy you desire.
When color management is enabled, more specifically when View > Use Display Color Management is enabled, as each frame is displayed to screen After Effects calculates a color transformation on the fly. This transform requires additional processor cycles and can slow down the playback performance; how much will depend on the frame requirements (dimensions, frame rate, bit depth) and your CPU speed.
After Effects can also use the GPU to perform this color transformation, by enabling the Preferences > Display > Hardware Accelerate Composition, Layer, & Footage Panels option. When enabled, there should be no performance penalty for enabling color management. Note that this option was disabled in After Effects CC 2015 (13.5) due to a compatibility problem between the new architecture and the GPU pipeline. This problem has been solved, and the underlying code quite improved, in the upcoming update to After Effects CC 2015.
Enabling video preview via Mercury Transmit has a similar impact to color management, that as each frame is displayed to screen it is also passed to the Mercury Transmit subsystem which consumes additional processor cycles to transform the frame for display on the second screen, and that transformation can cause playback performance to be impacted. This applies whether you're using a third-party card such as AJA. Note that Mercury Transmit is not accelerated by the GPU.
If both color management and Mercury Transmit are enabled, both processes will impact playback performance simultaneously.
I hope that helps.