The boarding party led by David Balme approaches U-110. Source: World War II Today
With regards to keeping the capture of the Enigma and codebooks from U-110 a secret (i.e. keeping the German POWs from revealing this to anyone), the German POWs did not know the U-110 was successfully boarded:
A number of schemes had been devised to capture these [internal Enigma rotors] but the boarding of U-110 came as an unexpected bonus. The U-boat had been forced to surface after depth charging, the crew had abandoned ship believing that the U-boat was already sinking. The surviving crew were rescued and quickly taken below decks so that they would not be aware that the boat was to be boarded. The commander of the boat Lemp died, possibly shot as he attempted to swim back to the boat to sink her. [emphasis added]
Source: World War II Today - 9th May 1941: Enigma Machine Captured
Upon recognizing the significance of what had been recovered, additional measures were taken by the British to keep this prize a guarded secret, to reap the most benefit from it:
The boarding party commanded by Lt David Balme made several journeys between U-110 and HMS Bulldog to collect whatever they could get their hands on inside the boat. This proved to be very fruitful, as U-110 was abandoned in a hurry, and being a Type IXB U-boat, did not sink as rapidly as a Type VIIC would have. It is almost certain that many U-boats were sunk as a result of the material found inside U-110, including an Enigma machine with rotors set and current code books.
The day after the capture, the British Admiralty realised the importance of this, and that if the Germans knew the boat had been captured, they would assume the worst and change their codes and cipher system. The boat was accordingly ordered to be scuttled while being towed to Britain, the surviving crew were taken straight to Iceland to be interned, and everyone involved in the capture sworn to secrecy. 15 of U-110's crew died in the action and 32 were interned. [emphasis and informational links added]
Source: Uboats.net
**Note:** The above is with regards to the OP's narrowing of focus to _[Operation Primrose](https://codenames.info/operation/primrose-ii/)_. In response to the earlier, larger question of keeping [_all of?_] the _Enigma "snatches"_ secret, refer to **[HistoryNet.com]com's](http://www.historynet.com/)'s [article** article on _Ultra_]**[_Ultra_](http://www.historynet.com/world-war-ii-ultra-the-misunderstood-allied-secret-weapon.htm)** and the **_[Safeguarding of sources](https://en.wikipedia.org/wiki/Ultra#Safeguarding_of_sources)_** section of Wiki's **_[Ultra](https://en.wikipedia.org/wiki/Ultra)_** entry. Both have details on the measures taken to safeguard the Enigma secret overall (_especially [HistoryNet.com](http://www.historynet.com/)_).