For a start, if the bird mites are as a result of something (or something wrong with) the common property, then you are not responsible for half the cost, the owners corporation is responsible for all of the cost. So I suggest that in any correspondence you make it clear that you are not paying for any of it.
If there is a genuine concern re mites or bugs or whatever infesting a lot because of a flaw in the common property, then the OC has to deal with it as a priority, not least of all because it is affecting the health and safety of residents. If it is affecting your tenants there is also a concern that you could lose them, with consequential loss of rent.
Write to the OC and say that you raised this in January and to date there has been no response, and that their failure to act may have a detrimental effect on the health and safety of residents. Unless they take action you will make an application to NCAT for an order for the work to be carried out.
Incidentally another thing you might want to think about is getting a pest controller in to inspect the gutters and give his opinion about how to deal with it.