When one says "I promise" should you trust them?

It depends on the person. Some say I promise as a force of habit; some say it to honestly reassure you because they are being nice; however many will use the phrase deceptively. You would have to think about the person and try and imagine when they would use the phrase "I promise". The thing about trusting someone is that you don't know if it is the right thing to trust them at the time, that's the whole idea of trust. It will help if you tried to get a profile of them, like if they usually say "I promise" when promising honestly, e.t.c. If it is someone who has truly gained your trust like you said don't be hasty to consider the phrase as if they are being deceitful, just try to realise they could just be reassuring you or making it easy for themselves to be trusted because they have honest intentions.