He had that argument with his Father and not Taylor, so technically he didnt know that Josh was so set on being treated as an adult. He should really have gotten at least some punishment that he will really remember.
I am not sure if Taylor knew about what Josh did. Logically there always was a chance that Boylan would talk about Joshs part in this, so not telling Taylor would have been very stupid, though in that case one would expect that he would send Josh to clean after Dinos for a year. Those Brachiosaurus outside of the Colony probably cause one or the other smell emergency from time to time.
Of course Taylor knew what Josh did or he wouldn't have approved the Boylan arrest. Not to mention he compares his troubled past with Lucas to Josh