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Cheaper breakers are garbage and not reliable.
Breakers are installed on each major power wire coming off the positive side buss bar. Rigs with inverters typically have three, really big units may have a fourth. Breakers for inverters typically are fused for the same size class T fuses protecting the inverter. The fuses fail first just like in a fuse breaker relationships.
Always select breakers to protect the wire size. Let the rig's fuse panel for instance protect it's branch circuits. You're seeking the protection of the wire feeding the fuse panel.
If the converter has it's own battery charging line connected to the positive buss bar then that line has to be protected as well. Again, protect the cable not the device. Converters have their own fuses.