Realistically speaking there are two ways of going about this as a potential issue.
Option 1 is giving Precog a brief window following a successful interrupt where it cannot be procced. Something like “Precognition becomes momentarily inactive for X-seconds following a successful interrupt.”
Option 2 is just don’t overlap kicks. Bite the bullet and accept that Solo Shuffle balance is already inherently skewed as a zero communication, zero synergy environment and either encourage people to actively seek coordination, or just set up an addon/WA to announce when you’ve kicked like we’ve had since TBC/WotLK and figure it out on a case-by-case basis.
I’m naturally inclined to go with option 2 on the notion that arena has always historically been an environment where communication is paramount (to such a degree that being consistently successful without comms is often held in high regard), and that undermining the baseline level of awareness required to play around something as fundamental as your partner’s interrupts would only serve to push arena further and further towards being M+ with an asterisk.