If an appeal is made to the EAT, they will notify the other side. This, however, is likely to take a little time, because the appeal will have to be processed by the staff there.
It is common to send a copy of their appeal to the other side at the same time at lodging it with the EAT. There is no requirement to do this, but it’s normally a good idea, since scrupulous good manners do no harm.
There are, however, circumstances when you might want to hold off. For example, if there is a chance that the Respondent will pay an existing award before learning of your appeal to increase it, but will become reluctant once they realise that an appeal is being made, you might want to put off the point at which they will learn of it. This is a tad ruthless, but perfectly within the rules.
The flip side of this is that, if you’re making decisions post-tribunal, you shouldn’t assume that the other side hasn’t appealed, just from their silence. If its important to you, ring the EAT who will be able to tell you whether an appeal has been received.