A small dose is injected into the fuel every time you fill the tank and coats the soot. The aim seems to be to assist in soot agglomeration (i.e. make it a bit stickier to give a large particle to catch) and to lower the combusiton temperature when the particle filter has it's periodic burn off or regeneration.
The particle filter is a ceramic matrix with a very large surface area. It's an impressive item, but is expensive to replace, although you would find information on possibly cleaning them on YouTube - use with care and consider the material as hazardous. I would NOT do this at home.
The amount of soot captured isn't actually weighed or measured directly, but rather inferred from the driving conditions since the last regeneration. Regeneration is triggered when the driving conditions allow (i.e a regular decent run helps if you only ever potter) and the soot loading has reached a suitable level. There is a differential pressure measurement as a backup trigger for the regeneration.
There is a small dedicated pump and ECU (mostly) and as the pump is probably not very good at varying the dose, the Eolys will possibly go further if you fill the tank rather than just topping it up.
No Citroen's were sold here with a particle filter prior to about 2005, so it eliminates the earlier DPX42 fluid from the local mix. I'd expect it's the same for Pugs, unless they were earlier users of the FAP here. Cars would have used 176 and then changed to Infinium and Powerflex (as the eBay listing suggests), depending on the model. The coloured caps noted are part of the connectors for the additive system. You can't mix Infinium and Powerflex, but they are designed to mix with 176.
As to the cost ... the Eolys 176 filling kit is more expensive than the Infinium kit, so Stuart's represents a useful saving for someone with a rigid tank. It still won't get around the need to reset the additive ECU, which needs dealer help.