There are two reasons you should pass this on to the strata manager. Firstly, they advised you to get a plumber in and secondly, it’s a common property issue.
FYI: This really has nothing to do with by-laws – it’s about what constitutes common property and the Owners Corporation’s (i.e. all owners, including you) legal responsibility to maintain and repair it.
On re-reading your posting, was it the strata manager, building manager or rental manager (if you are a tenant) who told you to get a plumber? I aslk because normally you wouldn’t ask your strata manager about a problem that appeared to be inside your unit.
Either way, the bill should go to the strata manager. And if you’re still not sure who does what you could do a lot worse that have a look at the Fair Trading booklet Strata Living to explain how things work in strata.