installing a 82-302 key tumbler in 1" thick door

How exactly do I install a 82-302 key tumbler. Specifically, does the retaining clip pull out with pliers or depress into the cylinder allowing the cylinder to slide into place and then pop back out to retain cylinder in place. I ordered a 82-302 to replace my old one (with broken tailpiece)and pulled the retaining clip out with pliers. A small spring flew out and the retaining clip won't lock back into place now.

A little "thinking outside the box" solved my problem. The replacement of the retaining clip with an appropriately sized and fabricated large paper clip worked nicely.
I'd still like to know exactly how the "original" retaining clip is supposed to work, though.
Thanks for your advice.

Thanks, Dave. That does make sense. Now I'll know if I ever have to replace another one.
Again, thank you.