Why did my basement start flooding while replacing sump pump?
You removed the 1 way check valve, likely part of the pump, when you cut the line to the pump.

Your sump being low, already had a syphon ready to go, it just needed one last push to get started.

The pump of one of your neighbors started and everything in the pipes of all 4 pipes came flowing into your sump.

Your son witnessed an excellent lesson in gravity and syphons. Far more impressive than anything he will be shown even in college physics.