Them contaminating us, or us contaminating them? It would be a sad sight to see if we accidentally kill any aliens we find with our microbiology.
Might be better at that point to live in orbital colonies to avoid killing the alien gardens we actually do end up finding.
Both. At the same time.
Bacteria and any analog by design and nature do not care what they are "in" beyond a very specific set of guidelines that define if they can survive or not.
IE if you have a bacteria that lives in something 50% or greater H20 and consumes an organic carbon(carbohydrates etc) then it wont notice an appreciable difference between the alien lake and your eyeball fluid. In fact to the alien(either way) bacteria the new host environment might actually be superior due to lack of predation and other risks.
A friend of mine more suited to this type of science once equated it this way to me:
Two alien ecosystems colliding is like taking all the bacteria from two entirely different biomes and putting them into a Petri dish together for that worlds most insane battle royal.
They might not care and chill.
They might wage nuclear war.
They might just pass the joint and trade DNA or whatever is on the menu that day.
Or anything in between.
/edit forgot something.
Living in orbit doesnt 100% ensure no contamination. Technic species are, by nature, epic trash producers. Something will eventually drop into that gravity well with a little bugger attached.