Overflow of hot water to rads???? advice

Just seeking some advice.:
I have central heating. I have a stove that heats the water. There is a towel rail in bathroom. This is fed from stove ONLY. It was put in when stove was fitted as a "overflow" in case of stove overheat.

I asked a plumber who serviced boiler recently the following:
Is it possible to feed two small rads from the towel rail as it was always very hot when stove was on. I pointed out two pipes exiting hot water tank which I had thought were linked to the towel rail.
Plumber looked at set up and said yes it could be done. He pointed out that when job was done stove would heat equally the towel rail and my new two rads(which are a short run from the tank) and the hot water , as before. That was the finest.

What is happening now is that , when the hot water which is set to come on every morning and the heating , these two new additional radiators are heating. I was very surprised to see this. Both systems are separate in their own right. This is not what I wanted or asked for.

All I simply wanted was that when the stove was on , and the towel rad heated , that the two new rads would heat also. The idea being it would save me having to put on the central heating at night before child went to bed , as the stove I thought would have heated the (new) rad sufficiently to take the cold out of the room.

I now find that when I put on the hot water , during the day a couple of times , these new rads are heating too , now its not as economical as it was before to heat the water as it is heating the new rads too. This has completely defeated the purpose of the exercise.
The new rads are small and are doubles and don't heat to any significant degree anyway , which is a nuisance ,however plumber has in fairness offered to change them for single rads , I am hoping that this will increase output or at least heat the rad from top to bottom , at the moment they are really not of much use (despite the towel rail being very hot all the time).
I am hoping if I turn of two one will at least get reasonably hot!
In retrospect this job was a waste of money really. Stove is 8KW.

I attach a couple of pictures and would appreciate feedback as to why the rads are heating when in particular when hot water is on? With windows open etc , its obviously cooling the temperature and the boiler is having to work harder to do the job it , and by extension , costing me more financially.
Sorry for long post!!