Hybrid Inverter Grounding Floating Problem.

Good day. I have a grounding floating problem with my hybrid inverter. It is a MUST brand 3kVA. On this inverter there is 8 terminals. 3 terminals for grid input (hot + neutral + ground), 3 terminals for AC inverter output (hot + neutral + ground), and another 2 is battery input (+ve & -ve). When there is grid supply as a primary source, the load will received completed circuit (by using socket tester all indicator hot + neutral + ground are lit). The poblem is when the grid supply cutoff, the battery source will take over and run inverter AC output, but at this moment the socket tester indicator only shown hot & neutral lit and no ground indicator. Why is the grounding floating when run inverter from battery but ok by using grid supply. For information the grid grounding and inverter output grounding is tap at the same point. Any body can help me or had any same issue. Thanks in advance. Very appreciate on that.