The down pipes are common property.
Though the particular pipe you mention is in one lot, generally down pipes service more than one lot ( you need to think about all the down Pipes)
In any case, write to the OC asking for the pipes to be fixed. Whilst the OC works out who is responsible for the pipes, the OC has the power to fix the issue, and then pay for it themselves , if it’s common property, or charge the lot owner.
There is little need for you to suffer.
An alternative is to ask the offending lot owner to rectify the problem saying that it is causing damage to your property and you will seek damages. I bet that lot owner gets onto the OC quickly. Now you have two fighting one.
BTW get another strata manager. The current one seems clueless.