OK, so that shows unequivocally that water from the F&E is entering your secondary water storage. There are there two possible explanations for that:
1. Someone connected the two without knowing what they were doing;
2. That feed into the cylinder is into a second coil that has perforated and is letting into water into the secondary water. A second coil in a cylinder, when present, is used for a supplementary heat source such as solar heating or a solid fuel boiler.
3. That F&E cistern is actually a small cold storage cistern. Naturally this would lead to a question about top-up water for your primary circuit, so it possible that your primary circuit is unvented?
In the case of 1 and 2 above, your potable hot water is compromised, tainted, and hygienic. If 3, then there’s still a mystery to solve.
Everything here is odd, so you were right to be suspicious about it. One of the many unexplained things is why no water flows from what you thought is the ‘main’ cold feed from the large storage cistern into the cylinder.