Do we still have to put manage this by moving track clips up and over others to make this work, or is there a feature like in Photoshop where you can specify that the adjustment layer only affects the track below it?
Ann is correct in the process to be used. An AL simply is a layer to hold instructions.
The PrPro processing chain is top to bottom in specific order of the Effects Control Panel for a clip on V1, then anything in say an AL on V2 or higher. So it's a "container" for additional instructions to be applied to the sequence at that point.
If you nest the AL and a clip below it, then you can get the behavior you want.