C.M.
Oh, my heart goes out to you! There is nothing worse than having to leave for work when your child wants you to stay (and you probably don't want to go, either!) First, I'd have Dad step up to the plate if possible on the safety issue of your son running outside after you. Even if you must lock the door behind you, he's GOT to stay safely inside. It's dark outside at 8 pm and passing cars certainly wouldn't be looking for a little one chasing mom's car into the street!
To address your son's issues, I'd try to get in a really good routine before you leave. This may mean you need to be ready a 1/2 hour before you need to leave in order to spend those last thirty minutes with him. Whatever routine you try, STICK WITH IT and when the time comes, BE FIRM and LEAVE! Kids have a sixth sense about when parents are on the verge of giving in, and if he knows you'll spend 5 more minutes with him, he'll do anything to get it out of you!
1) Try reading him a story every night before you leave..."The Kissing Hand" is a really cute book about a baby raccoon who doesn't want to go to school. So mama kisses his hand and he holds the kiss tight all day. Maybe your son has another favorite story instead.
2) Try setting a clock or drawing a picture of the time when you will be back home. Even though he can't "tell time" he can match up the picture with the real time and know that it is (or isn't) time for you to be back home.
3) Give him something "special" to hold onto until you get back...maybe a stuffed animal, maybe (if Dad doesn't freak out!) one of your old necklaces to wear...something that is "you" that he can have close to him. (But please don't let him wear the necklace to bed for choking reasons!) One of my sons went through a phase where he got worked up at school so I gave him a smooth stone to keep in his pocket. He could slip his hand into his pocket and massage the stone when he missed me and that seemed to calm him down and get him over that temporary hump.
4) Has he ever driven by your workplace? I don't know where you work or if it would be allowed, but maybe you could show him where you work (either the inside or outside of your building.) Maybe if he can picture where you are going, he won't be so scared that you won't return and feel safer because he knows where you are.
5) Maybe get a calendar just for his room that shows what days you work. If you go to work those days and he doesn't throw a fit, give him a big sticker on that day. Maybe so many stickers can equal some sort of reward.
Finally, you never mentioned how long these tantrums last. Do they go on for hours or just for 15 minutes or so? Is it as hard on dad as it is on you? Or are you taking it harder because YOU are the one that has to leave? Don't get me wrong, it's hard to watch your kids cry for any reason and the guilt caused by working can be tremendous. But it sounds like he is in good care while your gone, so I really hope one of these suggestions helps ease his tantrums and your anxiety!