The main question - should you expose to the right? - depends on how thoroughly you need to clean your sensor, and that depends on your style of photography. To find every dust particle that could possibly appear in your images, exposing to the right will give you the best odds. Realistically, unless you're routinely shooting large areas of sky or other uniform, light surfaces, for the same reason that the faintest particles are difficult to deliberately detect, there's a good chance they won't affect your images.
Why expose to the right? Exposing to the right captures more light, and thus more information, up until the point where highlights clip. This can help find spots that would otherwise be difficult to see. When you expose to the right, you're increasing the amount of light that the sensor gathers compared to the amount of noise: in technical terms, the signal-to-noise ratio. For the same reason that details are lost in the noise in underexposed images but not correctly exposed shots, increasing exposure beyond the metered neutral continues to increase the information about a scene that your camera captures.
Why did it have the opposite effect? Straight out of the camera, there probably won't be any apparent advantage. When you overexpose an ordinary scene, details appear washed out or low in contrast until you reduce the exposure in post-processing to recover the highlights, and the same applies to this situation. Shoot in raw and open the image in your raw converter of choice, then reduce the exposure to a neutral level, checking for spots becoming visible as you do. Increasing contrast may help. Some software like Lightroom includes a spot visualization tool that can also make faint spots more apparent (though unless your wall has a really flat texture, it's likely to produce a lot of false "spots").
The short answer to why this adjustment is necessary is that raw conversion has to take lot of information spanning a large range of brightness levels and condense it into an image that probably has contrast and detail in the right areas. This process doesn't represent every part of the range equally in the final image, and adjusting exposure is one way to control which parts of that range contribute the most contrast.