Historically jet engine fuel controls (think fuel injection brain box) had a “pressurization and dump” valve or “P&D valve”. For the fuel control to work, it has to have a head of high pressure fuel. After shutdown, this valve would open to relieve the pressure in the fuel control & manifold while the aircraft sat. The quart or so of fuel would vent overboard. Venting the fuel would also prevent it cooking into varnish inside the fuel control & downstream plumbing.
On startup, the valve is supposed to close immediately, before the fuel is introduced. So the valve closes, then fuel is flowed into the FC as the engine winds up under starter power. At some point the FC gets to full operating pressure then the main outlet valve opens and the high pressure metered fuel is released into the injection manifold, the fire starts, and we’re spooling up.
If for some reason the P&D valve is sticky, it can hang open during the early stages of the start and dump a quart to a gallon on the ground before it finally seals shut.
Back in the late 80s / early 90s P&D valves had to be modified to ensure they vent into the engine tailpipe area rather than onto the ground. That way the fuel evaporates invisibly into the air rather than dropping visible pollution onto the concrete ramp. Don’t blame me; I just report the facts, I don’t invent the rules.
There are also various overpressure relief valves which could open. But I’d expect that to be very rare and involve tablespoons of fuel, not quarts or gallons.
The A320 series aircraft are available with several different engines. Any one airline would tend (net of mergers) to have all one engine type. But different airlines will have different engines. So you may find the difference is that your drippy airline is using, say, the IAE V2500 engine while the non-drippy airlines are using the CFMI CFM56 or the PW6122 engine.
Bottom line: Engines ought not be dumping fuel on startup. But there are valves which can do just that.
One last thought. …
During a start attempt, if for some reason the engine doesn’t light off you will end up with a couple gallons of fresh fuel on the ramp. All engines have dual ignition systems, but most models alternate which system is used from flight to flight. One is plenty to start with and this technique evens out the wear between the #1 & #2 system.
If there is a maintenance issue with bad ignition systems, or an airline which is pressing on the repair rules, they might have a number of engines with only one functioning ignition system.
It’d be easy, depending on their crew quality & maintenance procedures quality to have crews repeately forgetting that, say, system #2 is dead on that airplane’s right engine today and only discovering that … again … after it doesn’t light off … again. So they dump the fuel, let the engine air out for a couple minutes, sheepishly switch to #1 ignition & try the start again. They’ll be successful (and gone) and you’ll have a spill.