I was shooting a scene, using a Canon 28mm 1.8, and after a few seconds I switched to a Canon 100mm 2.8, and the in-camera meter was suggesting different exposures! Why does this happen? Is this normal?
There are two basic possibilities.
First, and probably the biggest: the metering takes into account more of the scene with the wider angle, and the scene is different enough that the exposure choice is correspondingly different. This is particularly likely to be the case if there are actual light sources or shadow areas in the scene. You don't mention what metering mode you are using, but if you are using Evaluative Metering (matrix metering on other brands), the camera tries to recognize the scene and do something "smart" — but the algorithms are really not very complicated, and a small change can sometimes cause a big difference in what the camera thinks it is seeing.
Second, the lenses may have the same f value but different actual transmition. This is measured in "t stops" — more at What is T-number / T-stop? In this particular case, assuming you are comparing the EF 100mm f/2.8 USM Macro and EF 28mm f/1.8 USM, the former is about half a stop darker than the f number would indicate, while the latter is only a third darker. Assuming you're at the same f-stop, the difference between the two is small, but enough that you might notice metering variation. (If you have the L version of the 100mm, that's also about a third of a stop darker, so the difference should be almost nothing.)
The meter will adjust to the scene depending on what meter mode you have selected. Depending on your camera you can have it meter as much as the whole frame, as tiny as a spot under the AF point, or somewhere in between.
Let's say you have your 28mm on and taking a picture of something on your coffee table and the wide field of view gets the TV (which is on) in the shot. The light output from the TV may be influencing your meter. Put on the 100mm lens and now you've cropped out a lot of the scene (including your TV) which now isn't influencing your meter.
Also, there's a difference between F-stops and T-stops. They're usually pretty equivalent, but T-stops measure the light transmission which may vary from lens to lens slightly. If your meter is only slightly moving then it may be due to this.