I don't have a split system inverter to look at.... so this is guess work.
The PJ will use two transformers in series as the output. The center tap will be at 110v potential to either end of either transformer.
So you can have 0-110v with an 180degree out of phase 0-110v output.
You can have 0-220v with a center tapped neutral.
Neutral can be earthed the same as in the house system.... so there is no difference to the normal power
This should be identical to your street pole transformer in the US.
This diagram is from https://en.wikipedia.org/wiki/Split-phase_electric_power
The earth in the pj floats,( only connected to chassis ) and does not actually see earth until you connect to the main board in the house... then the chassis is earthed.
In 220v mode it is fine..... but is center tapped earthed as in the wiki picture... we don't do that over here.
We have one side of the 220 or 240v earthed as N, and the active s the other conductor.
You can do that with that PJ as well, but you can see that this will mean you cannot concurrently use the 110v outputs, and have them referenced to ground as well as the 220v... referenced to ground via a 220v neutral..... kaboom.... only via a center tapped reference to ground as per illustration.
So you should be able to use it as they do in the USA in that picture, for 110v and 220v, OR you can use it like the European and Australian systems do... but you can't do both at the same time, and have the earths doing the legal thing in both jurisdictions.
The other problem exists in the way the current sense works, as it will only see one of the split phases, or all of the full phase..... so you can o/load it without it knowing if you load up the non-monitored phase. The current sense is in the active leg of the 220/240v winding on the secondary. Power drawn on the other leg to CT will not be seen.
Battery charging will need to be done via 220v input only ( or grid tie on 110v or 220v outputs... not official )