Usually, though it is not necessary.
does it mean and the chords to be played are to be from that group?
The song Chura liya hai tumne jo dilko, starts off on Am.
And has chords Gmaj and Fmaj (I guess), you can be convinced that the song is in key of Cmaj or Amin (equivalent).
However, there is certain usage of chord Amaj also in teh song.
This example was just off the cuff, probably I did not list correct chords. But, for illustration of my point, it will do.
When one person suffers from a delusion it is called insanity. When many people suffer from a delusion it is called religion