They do not publish wall thickness on the performance tubing. It could very well be 1/8" inch but I cannot be sure as I have never measured it and the only person I know who tried it only got a couple days out of the tubing.
Precision tubing has a 1/16" wall so you can use off the shelf tubing. The one you linked is probably just fine. Looks like a pharmed BPT tube.
The wall thickness is critical as that effects how tight the rollers pinch it. An incorrect wall thickness either causes a no flow situation or a rapid tube rupture.
If you do purchase the tube from CP make sure you are getting a pharmed BPT tube as it has excellent life and properties. Also, if you do so, please measure the wall thickness with a set of calipers. 20' of tube is going to last a very long time! Maybe you can split it with someone who else who has a performance head.