This article has explanations and diagrams for a typical espresso machine. All the ones with the steam wand work similarly, as far as I know.
The steam wand is used to heat and froth milk for use in various
espresso drinks. This wand is connected to the heating vessel. When
the user puts the valve in the steam position, steam from the heating
vessel is released out of the wand and into the milk.
Regarding the heating vessel (or in the article, it is called a "heating chamber". I believe they mean the same thing.) it says:
The heating chamber also contains a one-way valve that lets water into
the chamber from the pump, but not back into the pump from the
So, it seems like steam only gets forced out of the nozzle and no milk goes into the nozzle back into the machine. Also, from the diagram, you can see that the steam nozzle is not connected to the part of the machine that makes the espresso.
Verify with your rav, of course. But, as far as I can tell, it seems parve. Of course, easiest thing to do since you're at the café is to ask someone reliable, there. You said it's a kosher café. Is there no mashgiach there or a supervising agency?