I ALWAYS increase exposure in RAW.

I find myself always increasing exposure in raw when I let my camera try and achieve "standard exposure."

Does this mean I should try increasing the exposure compensation so that the shutter speed is a bit slower? Or is it just the way RAW tends to work?

1) Based on the AF Area mode selected on your camera, it used a more or less large area of the frame to calculate an average exposure.
2) The exposure of a camera is based on level of gray, so if a subject is particularly light or dark this "average" standard exposure is always wrong (much or less depend from your subject).

Generally, on real world scenario, these average standard exposure is never perfect so you should almost always compensate it for obtain a more precise result.

The shutter speed should be sufficient for freeze your subject regardless other things.

The in camera meter (measures light reflecting off of the object) measures for 18% gray, when you take a picture of something white and the meter reads in the middle the white object will be 18% gray, if you expose for 1 stop higher it will be white with detail, if you expose 2 stops higher it will be white with no detail (blown out) -good for white seamless backgrounds, that is what the zone system explains

I just took a lighting class in school and practiced/learned ratios and the zone system, I also use a light meter to get correct exposure too by actually measuring the light falling into the subject (incident), I have been doing product shots lately

Also it would probably helpful if you look at your histogram as your shooting, then you could probably get a better idea of your quality/amount of light that is reaching the camera sensor