I really can't imagine a fault which trips the electrics being down to the plumber. A trip will normally trip due to one of three things, the surge being too high, unlikely with an element, the long term current use being too high, or the imbalance being too high. In my house are three are built into the same device, some homes the imbalance is a separate device to magnetic and thermal overload trip.
We have two main tools to check what has happened, the ammeter, normally a clip on type is used, and the insulation tester normally tests at 500 volt, we also have the RCD tester.
We are working with AC, so we have capacitive and inductive linking, and the insulation tester uses DC, so not a fool proof test, and the ammeter and RCD test needs power, so unless the electrician comes at the off peak times, it is hard to do a full test.
Economy 7 is a tariff not a system, when it first came out we had the white meter, and the immersion heater used for off peak was completely independent from any 24/7 heater. But people wanted to use washing machines and tumble driers etc on the off peak, so the system was changed, often it did have a radio 4 time corrected clock to trigger devices, but it was a trigger wire, or some times user set time clock to turn on the device.
We had a whole range of timers
each one slightly different, some with one supply, some with two, and one has to read carefully the instructions.
When I worked on Economy 7 the supply was normally taken to a fuse box, and there was no RCD protection, even when the main fuse box was changed for a consumer unit, often the off peak still used the old fuse box. I would think today the off peak does have RCD protection, and one thing I noted with my own fuse boxes (with MCB's fitted instead of fuses) was turn on the main isolator and often the RCD would trip, and I had to turn off the MCB's first then reset the RCD and then turn on the MCB's one at a time, but testing for earth leakage it showed no fault.
I see no reason why the inrush should trip the RCD, but I know it did, I can take a guess as to why, but it is only a guess, I considered all sorts, there is the X-pole RCD which it claims trips 80 - 100% rather than 50 - 100% and has some software to stop spikes tripping it, and also auto resetting now no longer allowed, but when I moved I went from 2 RCD to 14 RCBO's so each circuit is independent, and to date all trips have been due to genuine faults.
But it was very intermittent when the old system tripped, I could go two years with no trip, then have 5 in two weeks, nothing changed and then another 2 years fault free, so my thoughts are spikes on the supply, and now with a SPD fitted that is less likely anyway.
I have had trips, tested the RCD which showed A1, and to make the customer think I have done something changed the RCD anyway, and faults stopped. Which seems to point to spikes upsetting some RCD's. It seems not all RCD's are equal, but it is simple enough for the electrician to work out if some thing he needs to do, or the plumber, if the element passes the insulation resistance test, then the electrician needs to correct any fault, and if it fails the plumber needs to change it, however the electrician would say the element is faulty and needs changing, not simply down to the plumber.
So some thing missed from the tale.