Hey Jo,
when you say that the output is incorrect, could you clarify whether you are referring to the phylogeny of the run where you used bModelTest? If you are referring to the one with TIM, I don't think there is any reason why you should look at it at all. That being said, I think that the way you set it is wrong. I believe that what you have is four rate parameters, one for each rate except for AG and CT which are fixed to the start value. The TIM model has four rate parameters, but one for both AC and GT, one for AT and CG, and then one for each of the other substitutions left. I am not sure whether you can set it up in beauty, I'd modify the XML file by renaming, say CG with the name of AT, and fixing to 1 AC and GT, but again, why bother?
If you have issues with the phylogeny in the run where you used bModelTest, I think you may have other problems (perhaps the calibrations if you use some since you mention the dates).
It sounds like you used a starting tree rather than a random one because you say the phylogeny of the input data. Is it possible that simply your starting tree is not supported by your data?
Cheers,
carlo