A hybrid inverter in self-use mode tries to keep grid import close to zero. It measures power at the grid connection, usually with a CT clamp or a meter, and discharges the battery to cover whatever the house draws.
If the EV charger sits behind that measuring point, a 7 kW charging session looks like a very large household load. The inverter does not know it is a car. It only sees import and responds by discharging the battery, up to its maximum power.
The typical picture: the charger draws 7 kW, the battery supplies 3 to 5 kW of it and the grid covers only the rest.
This costs money even on a cheap rate. The energy in the battery was stored earlier, often at the same cheap rate or from solar. Moving it into the car during a cheap slot gains nothing. Later, when the rate is high, the battery is emptier and the house buys expensive energy from the grid. Every cycle also loses a few per cent and adds wear.
On a fixed overnight rate the effect can be small. With a tariff that adds cheap slots at other times, it can happen several times a week without anyone noticing.