If the engine mounts are indeed in good condition (and it can be hard to tell just by looking) then you might be looking at a problem with the idle speed settings. Engines typically idle more slowly when they’re cold and in gear and there’s usually a compensation for this. In an electronically controlled engine like the Sirion’s, this idle-up function will be a job for the onboard computer. But if the computer has lost the plot or isn’t getting the right signal from, say, a temperature sensor, then it can’t bump the idle up a fraction when it needs to. And then, once warmed up, the engine seems normal.

A cold engine that spits a little water out the tailpipe is completely normal. Water is one of the by-products of the combustion process. It’s black because it mixes with soot in the exhaust system. But we only see it when the engine is cold, as once warmed up, the exhaust system turns the water to steam and we don’t see it. A black exhaust in a modern car that runs on ULP is completely normal also.

Unlike fuel and oil filters which are often located in easily accessible places and are able to be removed and replaced easily, most automatic transmission filters are located inside the actual transmission. Usually, this means removing the transmission's pan which is also usually the way to access the transmission's valve body and other parts that are part of a transmission service.

The best way to access this area is to have the car on a hoist and work from underneath.

IT COULD be the plug leads, or the ignition coil, even a sensor. Have your mechanic check it again.