I guess generally speaking within what I do — «Design is the considered approach to aesthetics with a view to best communicate a message»In my opinion, there are two primary parameters that influence on how deep should a designer dive into the field of the project he/she is working on. The very first criterion is how experienced the designer already is in this particular industry. It is pretty evident that for highly skilled designers much less time is needed to grasp what the project is all about.
The second parameter is the actual size of the project. I am certain that the level of involvement does depend on the scale because you can hardly compare the time investment needed to familiarize yourself with a complex product dashboard versus a promotional leaflet.