For reference, there are tremors associated with Parkinson's but they are resting tremors. The initiation of voluntary motion tends to suppress them. Other conditions are associated with intention tremor where voluntary movement initiates or accentuates the tremor, but I don't think this is going to be an example of a tremor if he's able to play a guitar!
There are ways in which different kinds of body movements can be ingrained as group together into a unit intentionally or unintentionally and once grouped together, they can be forgotten. You don't think about the gas and the brake, you just drive. You don't think about the keyboard, you just type. Sometimes those connections can be well conditioned and difficult to separate. Think of how a dog kicks as if scratching themselves when you find "the spot".
An exam by a specialist may or may not be revealing but still reassuring, so it's not useless. Please note that many insurance plans require a referral from primary care for a specialist, so that's often where to start.
However in the future, without another clear direction to go, there are many sources of info on finger dexterity exercise. Basically any of them that are made difficult by this particular condition may be directly applicable to its treatment.
"If I have seen further it is by standing on the shoulders of giants." -Sir Isaac Newton
Armin Hanika 56PF