VFRSTAR
You got a lot of good advice here, especially Biggle's last comment re-visa.
On the score of the TTMRA - you will get issue of a equivalent licence ; despite being issued back-to-back. If you have a NZ licence, CASA will honour it.
However, for the life of me, I cannot understand why the school put you through a CPL flight test when you are applying for issue of an ATPL. The acquisition of a CPL is not mandatory before the ATPLA. Unless the instructor was checking your VFR skills which is required for a Circling Approach - a part of the CIR flight test.
There is no flight test for issue of an ATPLA, But you must have held, or currently hold, the Aus CIR (m/e) before being issued the licence. That kind of makes the CIR flight test the proxy for the ATPLA, so to speak. You need to pass CLWA, AALW and IREX exams. The CLWA needs to be done before AALW (naturally). These exams can be done anytime, and most do them all before the flying part.
ASL are the exam providers for CASA now and CASA have a link to their website on their own website (if that makes sense to you..).
So it sounds like you are nearly there in any case.
As others have mentioned, you need the security check (form 639 filled out and lodged) and an ELP (English language) assessment to do as well. Most CFIs have the CASA delegation to do this to level 6 only (you being from the States, the CFI will do). If a security check has not been completed by the time you finish the CIR flt test, you will have to wait until it is before licence issue.
Suggest that you start filling out form 196 off the CASA website which is the ATPL application form (I believe).