Realtime Update MySQL on every Update occurred on PostgreSQL
Two basic approaches. 

1) Connect the servers via ForeignDataWrapper, DatabaseLink, Linked Server, External Table, or whatever your source system calls their technology.

2) Replication

Replication changes can be collected by triggers, or puled from database logs.  High throughput systems should use a log based solution, although those usually cost money (Oracle GoldenGate, Sybase RepServer, IBM IIDR, etc).  You may want to check out https://www.symmetricds.org as an open source alternative.  

The downside to #1 is that your transaction success may (or will?) be dependent on BOTH systems being available.  Also, you will take a performance hit to update both systems at once.