On the invertibility of the TMAF projection

I've been using a couple of Affine transformer to transform data from/to a custom, local coordinate system. I just discovered the possibility of defining a custom FME coordinate system with the TMAF projection, so I'm trying to simplify my workspace using this. I put a new TMAF (based on UTM32) into MyCoordSysDefs.fme and then use it in a regular Reprojector transformer. It's my understanding that such affine transforms should be invertible, and that I should just need to change the from/to coordinate systems in the Reprojector to get the correct transform, but I can only get it to work one way? How is this supposed to work?