Stormwater and sewer are separate systems. Stormwater carries rainwater from roofs and paved areas to a legal discharge point, and sewer carries wastewater from inside the property for treatment. Which system a problem sits in changes both the urgency and the approach.
A stormwater line that is partly restricted will cope with ordinary rainfall and fail in a downpour, because the restriction only matters once volume rises. That is why these faults tend to reveal themselves at the worst possible moment and then seem fine again afterwards.
Common causes are silt and leaf debris accumulating in pits and lines, roots entering joints, a section that has sagged or partly collapsed, or downpipes discharging into a line that no longer has the capacity for them.
The practical implication is that stormwater is worth checking before a wet season rather than during one. Once water is entering a building, the options narrow to whatever can be done immediately.
If water is entering the house faster than it can drain, turn off the mains water, keep clear of any electrical fittings that are wet, and call for help. Do not try to clear a surcharging sewer or stormwater pit yourself, because the water can carry contamination and the pit may be deeper than it appears.