I work in trading, but mostly on the asian markets, so not sure about mifid. Usually the exchanges seem to give milli to second precision (which is very annoying: if Thailand says it's second-precision to timestamp their order executions but Taiwan says it's milli, our system has to use the most precise when ordering them and we get questions from our own multi market clients about why all these executions are seemingly simultaneous or why our system source marked the request at .480 while the exchange replied with 0.0 for the execution.
But, by no mean, does it mean we use special timing - but now that I say that, I realize I have no clue where our time signal comes from, clearly it wouldn't be the internet because our trading servers aren't exactly directly connected there, we must have an internal ntp sever o_O