Thank you for your answers !
Indeed this makes more sense, I was still not very familiar with the Mean Sea Level Pressure concept.
I found an interesting definition on the US National Weather Service website that mentions these anomalies :
MEAN SEA LEVEL PRESSURE: This is the pressure reading most commonly used by meteorologists to track weather systems at the surface. Like altimeter setting, it is a "reduced" pressure which uses observed conditions rather than "standard" conditions to remove the effects of elevation from pressure readings. This reduction estimates the pressure that would exist at sea level at a point directly below the station using a temperature profile based on temperatures that actually exist at the station. In practice the temperature used in the reduction is a mean temperature for the preceding twelve hours. Mean sea level pressure should be used with caution at high elevations as temperatures can have a very profound effect on the reduced pressures, sometimes giving rise to fictitious pressure patterns and anomalous mean sea level pressure values.