There are some questions to confirm with you.
How many BME280 sensors did you test?
Do you have a reference device to confirm the test temperature change?
In normal ambient temperature, could BME280 get the correct values?
Looking forward to your further information.
I only have one BME280. As you can see in the chart, I have an additional SCD30 as a second sensor an I have an additional thermometer to verify the temperatures. If the temperature is above 0° C there are no temperature jumps as shown in the chart.
Please see the following picture, which was from datasheet of BME280:
And BME280 temperature full accuracy range is 0--65° C.
The official product flyer says: full accuracy between: -40 ... +85 °C:
Full accuracy aside, I would at least expect the sensor to function properly in the specified range. And below zero it does definitely not.