There is a feature that tells Media Composer to compute and display an effect (for example, a dissolve or a Picture-in-Picture) whenever the Position Indicator is placed on it. This feature is called Render On-The-Fly, and is found in two locations.
The first location it can be found is: Special menu | Render On-The-Fly. When you're in Source/Record Mode, this feature is enabled by default. This is why when you place the Position Indicator on a dissolve (or another effect) that you can see it.
The second location you'll find Render On-The-Fly is in your Trim Settings: Project Window | Settings tab | Trim settings | Features tab. Here you'll notice that this feature is disabled by default. This is because it can often be frustrating to have to deal with seeing an effect (for example, a dissolve) when you're attempting to trim a shot. However, what if you're trimming a layered video effect you've constructed that includes multiple video tracks? In that case, there's a good likelihood that being able to see what is happening in the video layers as you trim would be helpful. So, now you know where to enable that feature when you need it.