If your larger tank (the one that supply’s the cylinder) is overflowing you should first check for float valve failure and replace or renew washer.
If float valve appears to be working correctly, you should then check the plumbing to your hot and cold mixer tap and / or shower.
If they have been incorrectly plumbed i.e unbalanced supplies, this will need rectifying.
What can happen is that the cold water (at mains pressure) is “overpowering” the hot supply and finding its way back into the cylinder and tank.
Firstly, turn off the cold mains and observe the effect on the cold storage cistern. The overflow should subside and stop within a few minutes and will confirm the diagnosis.
To rectify you should take a cold supply directly from the tank (below the hot water feed) to the offending mixer / shower.
This will balance the supplies and should cure your problem.
In addition, Water Regulations require that all mixer suplies are fitted with non-return valves. This alone would not provide balanced supplies though!
Non return valve.