Thanks. So it sounds like the electrician is running a 20 amp, 240 v circuit to the island and splitting the legs there. I'll verify that he's using a full size 2 pole breaker. However, There are still 3 things that draw 1500 watts (12.5 amps), so he's got to be putting 2 of them on the same leg for a total of 25 amps on a 20 amp leg. That's a 125% load and according to the circuit breaker trip curves
http://http://static.schneider-electric.us/docs/Circuit%20Protection/Molded%20Case%20Circuit%20Breakers/0100-400%20A%20Frame%20FA-LA/FA-FC-FH/0600DB0105.pdf (page 2) , that is in the manufacturing tolerance window of 2 to 3 minutes up to 2 or 3 hours before it trips. It does not seem like a good idea to me, but I can now see why he says it will work - he's hoping one of those 1500 watt items will turn off before it trips the breaker.
You hired the guy to do a job.
Not saying you shouldn't keep an eye on things, but unless you know what you are talking just making fuss.
Lots of things could be done. The wires don't even have to be on the same breaker. He could have one 240 V load, than wouldn't need the neutral sharing. He could have 2 120 loads, shared neutral. He could do a local disconnect and 4 circuit panel, doubt it, but could do it. He could use 4 circuit panel, and create 1 240 and 2 120 circuits.
How many watts is a 2 gallon water heater, 120 or 240? Dishwasher 120 or 240? Is the 2 gallon water heater part of the dishwasher, or just some point of use heater?
If he does use a 240 breaker, each leg is 20 amps. I am not sure you realize this. This is why work in watts not amps. Also you derate 125% for continuous loads, I am not sure if a dishwasher qualifies, because it goes through cycles. I may be wrong. But not everything is sized at 80% of capcity of the wire.
I get the impression you don't have a clue what is going on, and are just working yourself into a tizzy, along with other folks.