I know, it's horrible, isn't it?'
For the sentence, 'He said his Mum will be 50 on 15 December.', this would be the choice of most L1 speakers.
But for the second example you give, even though in the context 'tomorrow' hasn't yet happened, most native speakers would say
'I thought someone would be waiting for me when I arrive tomorrow.'
For your other example, 'I thought it started / was going to start at 9:00' would be the preferred choice.
It's an area that native speakers get completely tied up in knots about and you hear so many grammatical 'errors' when people are reporting speech.
Have you got any good self-study books for this grammar area? Michael Vince's books are quite thorough and give so much practice that you'll develop a feel for what sounds natural.
Student or Learner