It would depend on the circumstances. If Dany wants Jamie dead, Tyrion saving his brother's life would certainly be a betrayal.
I agree with your second point, but I've always thought that Jamie would be the one to finish Cersei. Tyrion could betray Dany (how or the extent of which is anyone's guess), align with Jamie, and the two of them could eliminate their sister: The stage is set with Jamie now knowing for certain that Tyrion did not poison Joffrey.