@Gwendoline1989 I'm afraid that your reasons for believing him that he doesn't masturbate just don't stand up in reality. Masturbating isn't the same as having an affair, when you would usually need to take a little longer, and it wouldn't be so easy to find somewhere 'safe' to have sex with someone else.
When at work men will pretend to need to do a number 2, and go into a cubicle in the men's toilets. When at home, if your bathroom has a lock on it, he will do it there, if it doesn't, and he feels the need, he will just risk you walking in on him. He could also do it in his car while it is parked - hopefully not too close to anyone else...
I just wanted to tell you that I have had partners that have told me that they have done the deed in their works toilets when they are feeling particularly turned on -which was something we could talk about without anyone getting upset. Of course it would not be as easy for a woman to masturbate in a toilet's cubicle, and I certainly wouldn't want to do so anyway, even if I had just been flirting with someone really hot at work!
If he does masturbate at work - which is very likely as you say that most of his free time is accounted for - then that is ok (eww, but ok). Of course, what isn't ok, is him lying about masturbating, and trying to control you, and he probably hopes it makes you feel guilty as well...