...That's not how that works. One of the relays is going to close first, and those set of contacts will take all the load. Similarly, one set is going to bear all the drama from breaking the connection (and with the motor, there's inductive kickback.)
The correct way to do this is to look up the motor rating for your relay and then size accordingly, not to do dumb shit like "oh I'll just double up these two relays."
Of course he fucks up and uses a resistor from mains to logic, too. Mains and logic should never, ever, ever come anywhere near each other. They're supposed to be physically isolated on a PCB, cutouts in the board, even.
Don't fuck with mains / appliances / HVAC / household water supply if you don't know what you're doing. This guy has no fucking idea what he's doing, and some winter day he's going to come home to a house that's 100 degrees inside and a flooded first floor (notice he didn't connect the water leak sensor?)
Home insurance is scummy, annoying, difficult and weasely in the best of circumstances. The second they figure out you had some chewing gum and duct tape hodgepodge running your dishwasher and that's what caused the flood, they will not only refuse to pay, they'll cancel your coverage on the spot.
Then you find out the joys of not having home insurance coverage on a house with a mortgage.
Edit: Holy christ I missed this part: "It seemed to be due to the push-on jumper cables either becoming too loose after years of jiggling or perhaps oxidizing and self-insulating a bit."
That is how you start a fire, people.