Turnage received the Large-Scale Composition Award for Hibiki while Dillon took home the award for Chamber-Scale Composition for his piece Tanz/haus Triptych 2017.
Scottish classical guitarist and composer Shibe received the RPS Young Musician Award, sponsored by PRS for Music.
Shibe told M: ‘It felt awesome to win. This award is a recognition of things you’ve done. It’s great, especially when you see the success of people who have traversed in more populist directions, you feel the more obscure directions you are taking are perhaps not so often rewarded, least of all physically.
‘So, to receive this kind of recognition is an important encouragement that what I’m doing is important and it is seen, and people do value it. Without that recognition, one wonders how many people would venture off in different directions. We have to be grateful for these things when they come along.’
Elsewhere, London Symphony Orchestra’s This is Rattle, which placed British composers and music at its heart, won the RPS Music Award for Concert Series and Festivals.
Highlights from the awards will be broadcast on BBC Radio 3 on 14 May at 7.30pm.
For the full list of winners, see https://royalphilharmonicsociety.org.uk/rps_today/news/rps-music-awards-winners-2018