Thanks for using the forum. I am happy to address your questions, and my answer will be based on the information you provided here. Please make sure you recognize that this forum is for educational purposes only, and it does not substitute for a formal office visit with your doctor.
Without the ability to examine you and obtain a history, I can not tell you what the exact cause of your symptoms is. However I will try to provide you with some useful information.
If your problems with your fingers occur only during specific tasks such as writing, one possibility is what is termed focal task-specific tremor or dystonia (dystonia is a specific type of muscle contraction). The task that could trigger the tremor could include writing, holding a phone in a specific way, holding a cup or other object, basically any specific sustained motion with the limb in a specific position. Performing the same task in the same position will repeatedly trigger the tremor/dystonia after a certain amount of time, but performing the same task in a slightly different position would not. This in your case would be called writing tremor, and your condition would be called primary writing tremor.
Some regard these task specific movements tremors or dystonias depending on the exact nature of the movement. The cause of these types of tremors or dystonias is not known, but they are usually isolated and benign, meaning that progression to a more serious neurologic problem is unlikely.
If your symptoms are severe enough to be bothersome or interfere with your occupation, evaluation by a neurologist, and specifically a movement disorders specialist, may benefit you. Sometimes, injection of a small amount of botox into the body part that is involved can stop the symptoms with minimal side effects.
Thank you for this opportunity to answer your questions, I hope you find the information I have provided useful, good luck.