Do I need to code my replaced injector?

Hello everyone!
I have a 2012 Seat Altea XL, 1.6tdi (CAY engine), and recently had to replace #4 injector. A local mechanic did the work for me, and got the car running again, but it doesn't run like it used to...
Now it has:

• a clicky-tappy sort of noise when accelerating, but quiet when cruising.
• a pronounced car shake when idling, which wasn't there before.
• Leak off pipe popped off 3 times while driving (squirting diesel over the engine) and required some reshaping of the spring clip to hold it in.

I've checked for leaks around the injectors, and to be honest it doesn't sound like that kind of noise anyway.
When I went back to the mechanic, ask asked specifically about whether he had coded the injectors, and he said they do not need to be coded. He also said that it would "settle down" after driving a few hundred miles.
Literally everything I've read about injector replacements says that they do need to be coded. The injectors all have the 6 digit alphanumeric code on them.
So I'm left with some questions:

• Can anyone here confirm whether or not they actually do need to be coded?
• Will it really settle down on it's own?
• Additionally, since it is a reconditioned injector that has been put in, would the injector code still be valid?

I feel totally out of my depth with this, and so not really able to argue with him, but it just doesn't add up to me.
Any help is greatly appreciated!

I'm not sure there is a forum here for your motor specifically.
FWIW, on the older TDI, the injectors must be "balanced" and pop-tested before installing. Do you have access to VCDS to check the injectors that way? The symptoms suggest they are out-of-sync, or the new one is not spraying properly.
HTH
EDIT: there are a few threads here about the CAY, and the best way to search this site is use a normal search engine, and input:
tdiclub cay

Thank you very much for your reply!

Following on from what you said, the search returned good results, so I bought a VCDS for myself, and found that the other 3 injector's codes matched what was stored in the computer, but the fourth did not. I updated this to what's on the new injector, and everything is now running sweetly!

Very happy!

Good to know and thankyou for the updated solution.