After some research I found out that the first shell, that runs on ttyS0, was configured to behave so in the /etc/inittab file.
This line in /etc/inittab was responsible for invocation of the default shell at ttyS0:
ttyS0::respawn:/sbin/getty -L ttyS0 38400 vt100 # GENERIC_SERIAL
So, based on my gut feeling, I put a getty on the second serial port by adding the following line in /etc/inittab
ttyS1::respawn:/sbin/getty -L ttyS1 38400 vt100 # GENERIC_SERIAL
It worked like a charm. Hope this helps someone someday.