It wouldn't be unusual for the rate change to apply without communication first, but it will follow. Your friend could contact to confirm the tracker has been restored, but the bank might not have other details just yet.
There are several steps to the process from the banks point of view. The first, once realising the tracker should be restored, is to immediately apply the rate change to prevent further overcharging.
From there, they need to calculate the amount of overcharged interest, which is a bit more complex as it requires a review of every transaction on the account. Most of this is automatic in a standard case, but requires a level of review and sign off, and gets complicated if the account was ever in arrears.
A letter would then issue with full details of the case, an offer of compensation, etc. I'm not aware of the normal timeline involved, but it should be pretty quick from this stage.