Actually, there are two potential issues with the Tera Player, high output impedance and capacitors in the output stage.
High output impedance (OI): The TP's headphone ports are rated 10 and 20ohms. This will affect the frequency response of IEMs with a non-linear impedance curve. Usually, dynamic drivers have rather linear impedance, like e.g. the IE800. If you look at the IE800's impedance curve (first graph), you'll see pretty much a straight line. That means the IE800 will not be affected by high OI. Now look at the 334's impedance graph, which is far from a straight line. That means the 334's frequency response will be affected by high OI and they may sound off as a result.
Capacitors in the output stage: The TP has been reported to having capacitors in the output stage and not being able to drive phones < 50ohms properly. The result is bass roll-off, which gets gradually worse with lower impedance. Note that this affects all types of IEMs, dynamic drivers as well as BAs. For instance, the 16ohms IE800 show a substantial reduction in bass when driven from the TP.
So, in a nutshell, BAs are hit or miss with the TP and all phones < 50ohms will show some bass roll-off. The 32ohm ones less severe so than the 16ohm ones.
While all this may sound a bit disheartening, the TP's shortcomings may actually benefit some IEMs, like the overly bassy IE800, which turn into better balanced phones when driven from the TP.