lets say you are running the inverter for the fridge ? or whatever
and you pull up and plug in to shore power
at the moment 120v is applied to the inverter-charger combo, it stops inverting and pulls in the 120v TS aka input relay, it might be micro seconds delay that you can't see but it shut off the inverter 120v out while doing the switch
in the reverse case, you are on shore power, and it fails
no incoming 120v, charging stops, invert comes on and TS relay drops out, to default to inverter power
in fact both TS switches change state, the house TS switch drops out the instant shore line power fails, before the invert TS changes state
the problem with the house TS and gnerator shore connection
is that it often fails by sticking one set of contacts
a 30 amp switch , switches (4) wires hot and neutral on each side gen/sp to the house input
a 50amp switch , switches (6) wires 2 hots and neutral on each side gen/sp to house input
when one contact sticks you end up with one wire from the gen and one wire from the sp connected to the RV
the gen becomes the path for the return side back to shore box
the gen is not in phase and cannot control the utilty input
it is forcefully tried to sync with utility power
the EMF forces involved are not trivial
this is a dangerous thing
usermanual
you type faster than I do