I believe, in the case of the J-10 pic we saw, the spin chute was only used during the prototype testing phase when the aircraft was pushed to the limit of its flight regime and in danger of stalling and spinning.
The way the spin chute is anchored to the aft of the J-10 is different from that of the brake chute. From what I can remember, there were at least three anchor points, at a distance from each other, at the aft of the aircraft to prevent spinning as opposed to the single anchor point of the brake chute.
I'm not sure if it is to prevent spins, as much as to recover the aircraft that are not responding to conventional spin recovery techniques, lots of trainers are intentionally spun as an integral part of training in order to teach recovery technique, the F-15, F-18, Su-27, Mig 29, F-22 would likely all spin and recover nicely, although spinning any fighter aircraft would be potentially hazardous without lots of altitude, I'm not so sure when it comes to an aft mounted delta with canards. Large aircraft are a totally different matter, although I have heard that someone rolled the Concorde, no one would intentionally stall/spin a larger aircraft, although the 707 prototype was rolled by the chief test pilot for fun!
As Master Delft has alluded to, testing in the 30s, 40s, 50s, and 60s was anything but boring, and no chief test pilot would roll anything unless he was retiring.
Back to the J-bird, we really have NO information about any test flights other than the few aileron rolls we saw with 2001/2002, although most fighter aircraft are rather routinely rolled, in WW II after returning from a mission a fighter pilot might perform a "victory roll" one for each enemy aircraft downed, they were forbidden due to the high attrition rate or the victory rollers under some commands... Brat