I'd be very careful too, sweetheart.
I might be a tad biased, because my ex-fiance did that right from the start with me, and I didn't pick up the signals, until it was too late, and he'd become very manipulative and controlling of me (everyone else could see it, but me - it took me up to 3 months before our wedding to see it)...
The point is, you still live at home with your parents (I gather from your post), therefore their requests should come first over your bf. Your bf should also be aware of this, and respectful of this. If he challenges this, then he is going against Biblical teaching. Even if you don't live with your parents, and your dad had asked this of you earlier, you had agreed to that, and it is good that you were upholding your agreement.
Is this a long distance relationship? Because I can understand that struggle when you only have a limited amount of time to talk. If that was why he got upset - then it's slightly more understandable, but still rude - he has to understand that you have a life outside of him, and other commitments as well - your life does not resolve around his contacting you.
If it isn't, and you live fairly close, then it is ENTIRELY out of line, and I wouldn't extend grace to that behaviour. 9 hours is not a long time. If he is restricting contact with you now because you had to hang up on him, then he's just being a childish fool, and chucking a tantrum - something that you DO NOT have to put up with. You are both adults, and should be conducting an adult relationship that does not tolerate things like tantrums.
I'm praying for you, and I would suggest you talk to him about this as soon as you can, so that he can understand that his treatment of you was out of line, selfish, and childish. Things like this can be big warning signs of controlling natures and childishness, so you need to have a strong talk to him about his behaviour being completely out of line, and explain to him why your life does not revolve around his phone conversations, and that you still have other commitments.
Please do not let it get swept under the carpet, or apologise, or excuse his behaviour. Make sure it gets talked about and resolved. If he doesn't see a problem with his behaviour, then that's a big red flag to me, and I think you'd have to have a big talk to yourself about whether you are willing to have someone like that in your life.
Big

and I pray it gets worked out. You did not deserve an argument from that!
Sasch
ps. Good books are the aforementioned 'Boundaries Before Marriage' (Cloud and Townsend), and 'Safe People' (Cloud and Townsend), which discuss a lot about 'cues' to determine controlling behaviour, selfishness and childishness - you'd be able to pick up both of these at Koorong or Word...