Well, if you are going to buy it from Briley, you'll be ordering "their" 2nd. generation tubes, but for the rest of the Perazzi world, you better make sure you are buying 1st generation factory tubes.
Just for the record, there is a pre-1st generation factory tube from the Ennio Mattarelli era, the Pre-mess-production choke tube installed in his 1968 Olympic gun, some of those short tubes were also installed in very limited number early guns, but those pre-production tubes are not available on the market. And it's not considered as 1st generation tubes.
Your 1st generation tubes were available from Giacomo Sporting at one time @$65 each, but I believe they are all sold out.
I don't know if "Perazzi" refers to the tubes as "generation or type", just what gun they are for. You can forget about the first ones they made, as they are rare enough that you likely don't have that gun, and anyone who has the chokes wouldn't sell them anyway.
Just give as much description as you can on the gun type (TM1, TMS, MT6, MX3 etc.), Top thread or bottom thread. Some one here is sure to help. And yes, the Briley 2nd gen per. is what you need.