If a regression model is predicting some monthly value, does it apply to last 30 days or to this calendar month during prediction time? I've trained a regression model to predict some process' monthly output based on monthly aggregated data - for example mean of January, Feb, March etc-.  The model doesn't care about seasonality.
Now, I want to use this model to decide whether this process has already output the predicted value in any given time. For this, I'm going to write a query against the database and compute process' output this month. But I'm not sure how to interpret "this month" in the query.
Should I compute the last 30 days or this calendar month? In other words, if today is July 1, should I retrieve only today's records from the database or retrieve records since June1st and compare it with the predicted value?

Your model only sees what you show it, and doesn't know any more. So if you've trained it to predict values per calendar month, it will predict values per calendar month and not in the last 30 days or any such arbitrary time interval that has not been specified in the model. The fair way to evaluate its predictions would be to compare the predictions against measured values per calendar month.
So if you want to know whether the model's predictions have been exceeded in your example, you should only retrieve records from July 1st and NOT June.
However, you also say that the model predicts the mean of each month - but it is not clear what this mean is. If the model is predicting the mean output per day for the whole month, you could compare the predicted daily mean (per month) against (i) the output of each separate day, or (ii) the mean output per day from a calendar month.
