Transferring songs from iTunes to iPhone
Alright I got ya.

iOS 8/ iOS 9

In order to sort your songs in your Music App on these Operating Systems, you have to:


Find under the tab "My Music", an arrow pointing down next to the text "Song", this is a drop down menu, tap it.
It will bring you to a list where you can select the sorting method, there are several options you can choose from here.
Finally select the option "Album" in order to sort every song in its own album.






iOS 10

I'm with you, sorting songs on iOS 8/9 can be not intuitive or fast to use, but there are great news!
In the upcoming iOS 10 update (coming this fall) the whole interface of Apple Music has been redesigned. 

So, now in order to do what you asked for, it will be as easy as opening the Music App, tapping the "Library" tab, and finally tapping on the Album option to see all your songs sorted in their Albums.
Take a look at the new cleaner design: