There are lots of gizmos and gadgets that keep a modern engine running sweetly and maximise efficiency, and some of these do involve the camshafts. But I’ll go out on a limb here and suggest that the component you’re referring to is the cam-chain tensioner which does, indeed, operate automatically to keep the timing chain at the correct tension. Why am I so sure? Because this series of engines has a terrible reputation for premature wear of these components and subsequent replacement of them.
Shared with both Peugeot and Mini, the engine in your car experienced timing-chain problems (mainly a stretched chain) in both turbocharged and non-turbocharged variants and became obvious when the engine started making rattling noises, especially on cold start-ups or when idling. Eventually, the chain could fail and if this happened, the engine could be destroyed and would need to be replaced. The solution was to catch the damaged timing chain components before they became a problem, and that’s where having a listen to the engine each morning comes in. Beyond that, you can reduce the risk of the problem occurring by changing the engine oil every 10,000km (and not stretching this interval) and keeping a close eye on the engine’s dipstick and replenishing the oil to the correct level when necessary.
Peugeot kept fiddling with this engine to try to fix this problem and developed no less than four different timing-chain designs over the life of the unit to try to fix the problem. But none of the fixes seemed to be perfect, so it’s an ongoing thing. The build date of your car will determine which design it uses, and the bottom line is that sometimes you can get away with replacing some of the timing components, while at other times, you’ll need to replace the chain, tensioners and seals…quite a big and expensive job.
Assuming the worst, you should budget for at least $2000, maybe more depending on what workshop you use.