In my opinion I do not see what difference it would have made if no one told the timer to start the 30 second clock. Yes it is recommended, but that does not mean it is required that the non-calling official go over. Sometimes sending the non-calling official will cause more problems because the coach is more upset with him/her than you. Also both of you could have slowed down a bit. You should not be shooting FTs until the DQ'd player has been removed. This more like a case of not very good communication (with the table as well) and going too fast.
I bet this situation will not happen to you again.
Peace