Before the American Civil War, if one was a Northerner stationed South

US Army and Navy personnel remained US troops until they left the service. For officers, this meant resigning their commissions. They could them join the Confederate States forces. Enlisted men would have to complete their enlistment obligation regardless of their wishes.

Few Army bases at that time were in the South. Most of the Regular Army was out West to prevent or react to Indian uprisings and mainly stayed there throughout the war.. Where Federal forces and State forces came into conflict, like at Fort Sumter, Union enlisted men did their duty until killed or captured. Captured US soldiers were then treated as POWs. USN and USMC personnel simply stayed on their ships which redeployed to Northern ports.

if one was a Northerner stationed in the South, would he automatically have to fight for the Southern cause when it started?

No, nor the other way around. Col. Robert E. Lee, for example was stationed in D.C. when the war began and was offered command of what was to become the Army of the Potomac. Instead he resigned his commission and returned home to Virginia.

IIRC Gen. George Thomas, the later "Rock of Chickamauga" and a Virginian, was serving in NC but came north and remained loyal to the Union.

On the other hand, Gen. John Pemberton, a Pennsylvanian who had married a southern woman, resigned his commission and went south where he later surrendered the city of Vicksburg.

As far as I can tell, one took an oath to serve the particular cause and was sworn in

There's a very early scene in Gods & Generals in which a young Pennsylvania man is enrolled at VMI. Jackson gives him the opportunity to resign from the school and return home with his father. The student declares his intent to remain, after which Jackson warns him that if he stays now then decides to go home later, he'll be treated as a deserter.

I'm assuming that the people of 1860-61 were very aware that civil war was possible or even imminent; the powder keg was full and spilling over and only the spark, Ft. Sumpter, was needed. I doubt many people thought the secession crisis wouldn't turn to war.