Multi fuel stove alongside oil heating

Currently getting an inset boiler stove installed to run alongside the oil central heating. I'll never run both at the same time. We had an open fire before but wanted to get heat to the radiators and some hot water which is why we opted for a stove. The plumber is changing the cylinder also to a dual coil one.

My question is when the oil is on by itself will it try to heat the water that's in the stove? This is I'm guessing the same water that's in the radiators so what's to stop it doing this? It'd be very uneconomical if it was to heat the stove as well as the radiators.

No, the coils for the boiler and stove will be separate with separate circulation pumps. The pump on the stove back-boiler circuit will only run when the stove is hot enough.