Pgbouncer+Stunnel mixing up connections to Amazon RDS Postgres

Here are my configs.

I have two databases on RDS Postgresql. I have Stunnel listening to a single port (8432) and connecting to RDS.

I have two databases defined in pgbouncer. I have a gunicorn + gevent + flask stack connecting to these two databases separately. Meaning stack A connects to DB A and stack B connects to DB B

Everything connects and works fine - but after some time (or after a redeploy), the database connections seem to be crossing over. For example, stack A seems to be getting results from stack B, etc.

I tried a whole bunch of things, including having separate pgbouncer instances for both databases, but still this happens. Is this something that Amazon RDS is doing ?