Last year, I started working with the company I am still with (and a place I had worked for previously, as had a number of others I knew) straight after Spring Festival (which, if you'll recall, was late February.
I didn't leave here until May 20th or so, to fly home to apply for the Z visa!
(I lost about 2-3 weeks due to the Criminal History Check bit).
So, yes, it's a total PITA, and it can take a long time!!!
OP is trolling! Proceed with caution!
He's keep repeating Qs about FEC, despite difference between FEC and WP was explained 'brazillion' times, and he/she never entered China.
What is the name of the School, which mail FEC and Invitation letter in two separate mailings?
Tell us, how your FEC looks like? Did your 'activity FEC' arrived with regular or express mail service?
Once you have your FEC then the working type resident permit is pretty much a formality providing all the paperwork is in order. You will have a month to have this completed after entry. Depending on the city, it can take up to a month to receive your resident permit. So I would suggest that you get the ball rolling asap upon arrival.
"Activity Director" may just be their job title for "Dancing & Juggling White Monkey/ Foreign Teacher". You will understand soon enough.
Keep in mind that Chinese people may know "academically" ,that this needs to be done but will piss about getting it done unless you push them a little. You will hear "Don't worry, it will be fine". Do not trust this.
Upon your visit to the Entry/Exit guys, if the paperwork is in order, they will give you a receipt telling you what day to return to collect your passport. You have to pay by card so open a bank account as a matter of priority. Your school will probably have a bank of choice.
Good luck and wait for the cynicism to begin.