Hi,
I'm starting at the end - assuming you wanted positions in WGS84 all is good.
If you want positions in the NZ local geodetic frame (NZGD2000) a transformation is missing (at least if I understand everything correctly).
What type of positions did you expect - and what correction source did you use? And is there any reason (aka shift) which triggers you suspicion something is wrong?
Details:
I'm answering in steps so I hope I don't miss too much...
First - the datum... I assume you used SBAS or RTX as correction source.
With those two correction source types you get positions in ITRF2014(current) - which is EPSG 1165. This is equivalent to WGS84.
TMM only corrects for geodetic datums - so shifts introduced due to plate tectonic and such. There is also an EPSG 1165 for Eritrea - but this is a coordinate transformation.
EPSG IDs are only unique in their category - so you can have the same EPSG for different things... I think thats whats causing the head scratching.
Next part - EPSG 4326 is WGS84. WGS84 on the other hand is based on ITRF2014 (or the global and time dependent reference frame).
The ITRF2014 frame we have in the TMM drop down refers to the reference frame of ITRF2014 - meaning ITRF2014(2010), the creation date of ITRF2014.
In contrast WGS84(current) translates to the current TRF2014(2020.04) at the moment (16.1.2020).
I'll ask one of our NZ guys to be on the save side - but assuming WGS84 was your goal all should be good.