ISS “bracketed” by 4 moving objects that looked like regular stars..

Was floating in backyard pool, lights off, looking up at sky directly above me. Saw a slow steady bright “star or planet like object” heading from SE to NW. I thought it might be the ISS, and when I later went in I confirmed there was indeed a 6 min flyover that I just was lucky enough to catch. The unsettling part was when the ISS was directly over my head, I could see the stars behind it as it past by them, those stars (4 in this case) actually moved and absolutely “bracketed” the ISS as it moved across the sky. Almost like a targeted object in a scope. So the 4 “stars” were positioned at a (12, 3, 6 and 9:00 position) around the moving ISS. MOVING WITH THE ISS, the stars moved with it for almost 20 seconds. There were no clouds in the sky ( I made sure of it after the event), as sometimes moving clouds make stars look like the stars are moving. At the end of the “bracketing “ timeframe, the ISS moving towards the NW sky and I knew I’d lose it soon…but bef! ore the ISS was out of range, the 4 “bracketing stars” each moved outwards at same time from their prospective compass points (12:00 went up, 3:00 went right, etc) to form a larger bracketing diamond. Keep in mind they just looked like stars (same dimness as background stars in night sky), but just after they widened their bracket, the stars randomly moved in all directions and stopped dead in the sky, meanwhile ISS moved on to the horizon and started to dim. One last look at those “stopped” objects and they blinked out 2 at a time. First 2 just disappeared then within 1-2 seconds later, 2nd 2 blinked out. Couldn’t believe what I was watching and I know what I saw was not stars or my sight being weird. Would be interested to know if the ISS or radar picked up anything at that moment, since I know exactly time and area (based on ISS Flyover time and direction.