My wife's car is a 2013 Holden Cruze. Over a year ago oil started seeping into the engine coolant bottle as well as the radiator and subsequently through the cooling system. She was informed this is a common issue with the Cruze and was primarily due to a mix of metals/alloys in the cooling system where one material degrades and eventually a leak occurs. It was quite a costly repair. Is this a common issue with the Cruze? Holden avoids responding to the question.
If the car in question has the 1.8-litre engine, then this is definitely a known problem. Plenty of these engines suffered cracked cylinder heads which could allow the engine's oil and coolant to mix, producing the symptoms you saw. Holden actually issued a service program to replace the cylinder heads and other components to address the problem.
The other major cause of these symptoms is a failure of the transmission's cooling system. This actually piggy-backs on to the engine's cooling system (they use the same radiator) but if the transmission cooler fails, it can allow transmission fluid into the radiator and coolant into the transmission. Eventually, this will destroy the transmission both mechanically and electronically.