How do meteorologists know what the pollen level is going to be in the future? What factors are used to predict this in a specific geographic area?
The same way weather forecasts are done; you look at the current situation and draw from your experience what the most likely future situation is going to be.
For example, rain is going to wash down pollen from the air (and plants release less or none), so pollen level is going to be low. Dry air and sunshine makes plants release more pollen and makes pollen stay in the air for longer, causing more issues. Different plants release pollen at different times of the year, and in different conditions.
For any given region, you also know which plants exist, and you also have data from previous years. All of these are used to make predictions.
Trees release pollen in specific conditions and at specific times. And they will have a general good idea of what trees are in the environment. So it is just a matter of looking at what conditions coming up thar will cause pollen to be released and then warning people.