According to 'Dictionary of Basic Japanese Grammar', this usage of で "indicates the time when something terminates or the amount of time a period of activity has taken" (p109).
This was mentioned recently in another thread here. The default particle for marking a point in time is に, generally corresponding to the English word 'at'. This indicates that the named event occurs at the named time. It is possible to use で to mark a specific time, but doing so changes the meaning slightly. Using で instead of に indicates that the point in time is the end of a longer period of time which came before it. The named event is now understood to be the culmination of a longer period which preceded it. Your sentence 来月で30歳になります includes the understanding that it is a culmination of a previous time period (your life up to age 29). Likewise, 来年で辞めるつもり includes the understanding that the event (quitting the job) is the conclusion of a longer event (working that job until the final day).
In other words, events are normally marked with に, but if you want to include the idea of that event marking the end of a longer period of time, you can use で.