In summary I pointed out:

• You are right - of course you have to be relaxed when serving, but you don't have to be as relaxed until you start the throwing action which is the taking of the racket into the back-scratch position.
• That part has to be done in a very relaxed action because you have to rotate the wrist to do it and therefore the answer to your question is yes you have to be relaxed throughout your action but especially the part known as the throwing action.
• you appear in training to be doing it absolutely perfectly but it does sound that you tighten a little when get into match play, but you can't allow this to happen- you've got to get that relaxed feeling.