“Calcium chloride compound” is just a shorthand for a mixture of calcium chloride (~95%) with balance being potassium and sodium chloride. The material is derived from ocean salt so there's always contamination with other chlorides. Reagent grade (high purity laboratory stuff) is made by other methods. There are two possible explanations (conjecture, really) for why adding CH increaser might affect FC and it somewhat depends on how you add it.
First, CH increaser will increase chloride ion content which is what the SWG uses to produce chlorine gas by electrolysis. A large "slug" of chloride, either in the form of solid granules or pre-dissolved concentrated brine, could makes its way to the plumbing and cause the SWG to temporarily sense a high salt load. Many SWG's will stop producing chlorine if the "salt" sensor goes very high in order to protect the plates and the SWG from passing too much current. It's somewhat unusual, but it can occur. Depending on how the SWG operates, it may shut down production for an entire cycle or until the unit is reset. That would cause a perceived chlorine demand because the unit would stop making chlorine. Dense brine solutions don't mix well in cooler water and so it's very easy for the brine to pool at the bottom and get picked up by the main drain. We see this all the time when people add salt to their pool and then the SWG's go crazy with high and low salt warnings.
Secondly, and bit less likely, there is a chemistry effect too when adding a lot of salt all at once and it has to do with some complicated chemistry principals. Essentially, a large load of salt will cause the ionic strength of the solution to increase and, in the case of calcium chloride which is very soluble in water, it can increase a lot. When the ionic strength increases it changes the equilibrium constant for the reaction that balances hypochlorous acid and hypochlorite anion. I have not looked at the detailed math yet, but it may be that a large slug of CH increaser changes the equilibrium enough so that the amounts of active chlorine species differ significantly. Hypochlorous acid and hypochlorite have different rates at which they breakdown with hypochlorite anion being much more susceptible to UV photolysis. Again, this is all conjecture at this point but it's not outside the realm of possibility. A large amount of solid CH increaser would create a mass of water around it that has a salinity close to the solubility limit of the salt and a dense brine solution could cause a similar effect. Heating is also an issue but only when one adds solid CH increaser without diluting it first. Not my go-to explanation for things, but chemistry gets weird when solutions are concentrated and pool water is far, far, far from an "ideal solution" upon which lots of chemical reactions we care about happen.
I do believe you when you say that you are measuring an extreme FC loss with addition of CH increaser. Thankfully it's a transient phenomenon. Just keep adding FC from an external source like liquid chlorine until the loss rate normalizes. In the future, you might simply add less calcium at any given time or use calcium hypochlorite (and shutoff your SWG) to slowly raise CH. There's no harm in doing that.
