Hello,
Rob hit it on the head.
For the evaluations, what they focus on mainly are PFTs (FEV, FVC, etc), medications, and doctor visitations. With the doctors visitations it is not so much just regular check ups as it is in seeing any exasperation's to your condition that you have experienced. (Think ER visits, secondary conditions related to Asthma, etc)
Make sure you provide or have readily medical documentation showing that you are prescribed medications to control your asthma and that you are compliant (pharmacy refill record) in following the care plan and also any periods of exasperation's that required medical attention, if any. Hopefully you are under control enough that ER visits are not a regular part of your routine.
The pulmologist is great for diagnosis of your condition and coming up with a therapy plan for your asthma since they are one of the specialists in that field. If your current care plan has your asthma under control, then a regular PCM is fine for following through and maintaining that care plan. If your asthma, though, is not under control then it would be wise to speak with a pulmonologist / allergist not for TDRL purposes but for your own health to see if there are things that they can do to help tweak and improve both your care plan and in the process, your quality of life.
Some people wonder if their asthma is under control or not. The forms you fill out before visitations usually ask the same three questions: do you wake up wheezing at night, how many periods of exasperation have you experienced in a set time, and how many times have you used your rescue inhaler in a set time. If you answer yes to those and put a number that passes a certain point or just even answering yes I was informed by the allergist considers the asthma uncontrolled and their goal is to get the individual to answer no or as little as possible to those questions.