I don't have an adjustment period with songs. However, there is a point with listening to a song, where I will be really listening to it, as in paying attention to it, and it will imprint some impression on me, like a story or a feeling or an image or something. Often songs by the same artist will give me similar feels.
For example, Erik Satie's work mostly makes me think of forests, with tall trees and lots of very green plants covering the forest floor, and clearings in the trees filled with wavy grass and other plants. The imagery is much more in depth than that - that is just a small description.
Some of his songs, though, make me imagine being inside a very old house that was left alone abandoned for a long time, with beams of light shining through the dusty air, coming in either between cracks between boards or through windows. Listening to these songs, I imagine myself in this place, huddled in a small space - and it's not uncomfortable at all, it's actually really comforting and such, but there's also a feeling of the place having once been filled with life and things happening, wishing it still had people inside, remembering the many years where it did, while it sat there alone for countless years. It's a warm feeling, not temperature-wise, but just warm textured. I don't know how to describe it.