I haven't used his kit. I only ordered a couple things from him and sourced all the other parts myself.
The red mushroom button should not stop or kill any process. But it should hault all processes on both sides 220/110. Once the button is turned off, everything should continue as if untouched.
If yours is only deactivating power to some output devices, the unaffected devices don't have the power routed through the E-stop.
The E-stop should be on the controlled side of the 15a breaker and it should contain an NC contact block on the side when the button is not active and an NO contact block on the active side. All the power running to the power side of the contact blocks on all your switches should have the power coming off the NC side of the e-stop. They should be daisy chained. See the red wires on the door panel. They jump from one block to the next on all switches. Top row of 3 are the elements 220v side. Bottom two are pumps.
The E-stop inactive is allowing current because the block is "never closed" so it faults on. The E-stop active side is "never on" so it faults off. Once the NO side is on, it moves the power to the red LED and cuts power to all contactors and pumps.
110v power is used to turn on the contacts and thus providing 220v to the elements. The pump side doesn't have a contractor because it only needs 110v. When the E-stop is triggered, the 110v activating the electromagnet to the contactors shuts down thus cutting the 220v power to the element. And of course it's cutting the 110v to the pumps at the same time. The BCS will still assume everything is running since it can't detect the current. So once deactivated, all power is back and the process continues as nothing happened.
Sometimes understanding the action helps to understand the reason behind the wiring. So hope that helps.