He attributes his early determination to become a trumpeter to hearing Roy Eldridge's solo from a Jazz at the Philharmonic concert.

He has cited Dizzy Gillespie, Lee Morgan, Freddie Hubbard, Kenny Wheeler, Woody Shaw, and Clifford Brown as early influences.

Presencer worked with British musicians Peter King, John Dankworth, John Taylor, Ronnie Scott, Norma Winstone, and Mike Gibbs, as well as with international musicians, including Johnny Griffin, Chris Potter, Mark Turner, Niels-Henning Ørsted Pedersen, Randy Brecker, Red Rodney, Herbie Hancock, Chick Corea, John Abercrombie, and Bob Berg.

[4] Presencer has collaborated frequently with contemporary classical music composer Siobhan Lamb as an improvising soloist.

As a session musician, Presencer has recorded with Sting, Jamiroquai, Zero 7, James Brown, Ray Charles, Joni Mitchell, and Jonny Greenwood.