If I were the HR Head of Company 'X', I would definitely write to Company 'Y' on this subject because it is a breach of trust not only with Company 'X' but also with Company 'Y' (because you have informed Company 'Y' that you were relieved by Company 'X'). If you had fulfilled your commitments and Company still did not relieve you, then it would have been acceptable to join Company 'Y' without being relieved, but from what you have stated, it seems that you have not done so.
Again, if I were the HR Head of Company 'Y', I would take it seriously because if you can do it with Company 'X', you can do it with Company 'Y' as well, and ultimately, both are employers.
KKT