The Mikunis have only a mixture-enrichment device - similar to Weber DCOEs. Rather than running the mixture enrichment until the engine's warmed up, as soon as it starts, I pull out the hand throttle to 1500 rpm or so, then push in the mixture enrichment. Trying to keep extra fuel off the cylinder walls. So yes, it's separate from the mixture enrichment.
It's like a motorcycle - you enrich it to start, then once started hold a little more throttle until it's ready to go. Since these carbs were originally made to replace SUs on Harleys, that's probably how they do it.