You keep saying the porn on the phone makes you uncomfortable, do you know why? Most phones are like computers now anyway so what part of the whole phone thing makes you uncomfortable?
Also it could seem this issue you are having is a sign of something deeper ie such as him not respecting your feelings in general so maybe examine those other times he hasn't considered your feelings and see if they make you have the same reaction as the porn thing.
As for whether he keeps his promise to keep porn off his phone or not well we can't tell you what decision to make if you do decide to snoop and find it there. Snooping isn't healthy in a relationship either. Definitely indicates distrust. Be careful too coz if you tell people what to do (or what NOT to do) it forces them to become more secretive, in fear of them hurting you. Keeping things as open and honest as possible is the key. If you feel your feelings aren't being respected, whether its the porn or other issues, then you need to decide if you deserve that or not.
Good luck.
Some people are drains and some are radiators... Keep clear of the drains and hug the radiators!