If what you say is right, that means your meter is off by 4 stops. They are supposed to agree pretty closely. If you have an 18% gray card and stand in front of it. Place your meter in incident mode and point away from the gray card and read. Then, place your meter in reflective mode and point to the gray card and read. Both reading should match pretty closely. Just be careful of your own shadow. You shouldn't have to compensate at all.
But, since you said your meter was professionally checked and calibrated and it's your first time using any light meter, I think re-checking of checking method is in order.
I have a L758 and I've only used 508 few times, so I'll have to look up where the controls are.
When you go from incident to reflective/spot, you need to switch the meter. The switch is located on the right side of the meter and around the eye piece. You rotate it. Are you doing that? When you do, at middle top of the display, dome icon for incident and something that look like a triangle for spot should show. Does it?
Let's do that much and see....
By the way, let's take your DSLR out of equation for now. It's not calibrated to 18% and we need to first check if your meter agrees with itself.