I don't realy mind about such things nowadays, but when I began learning guitar , I was told to anchor my fingers specialy for pull-offs , and it helped.

The most important thing about pull-offs is to make sure that finger you're pulling into is in place just before you pull.

Also for picking , you should have your fretting finger in place just before you pick.

So when you're playing a chromatic chop like the example you mentioned (wether you're picking or making a legato) , you don't have to anchor the three fingers at once, just make sure that each finger is in position before it's played.