Is your greyscale K only or is it a RGB greyscale? Well, in fact I know it is the last ;-)
And effect on a page shows RGB images in CMYK simulation (according to your colour management profile settings). To avoid this on screen change your colour blending space, but I advise you not to as the simulation is closer to a CMYK print. Learn also how to softproof your document (you will see the same effect on your RGB images).
Consider making the greyscale images 'real' greyscale, K only.
Thank you. I checked the TIFF photo and it just has one channel (black). Is
there some other place to check?
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ID does not support Grayscale profiles and puts the image on the Black plate of the CMYK working space using wahtever numbers are saved in the file. this can result in a image that is either lighter or darker than you expect looking at the image in Photoshop. The addition of transparency forces ID to display the preview accurately according to the separations, so some shift could become apparent. For the absolute most accurate grayscale conversion, create a color settings file in Photoshop that uses the Black Ink channel of the destination CMYK working space in in ID. To do that, make sure the "more Options" has been selected in the edit color settings dialog in Photoshop, then choose Load Gray from the Grayscale dropdown, and finally choose the CMYK profile you want to use.
Ah... And there was, so sure it would be RGB... If it is a K one channel only TIFF it depends a bit on your colour management settings, in 'normal' situations your CMYK values (so K only as well) should be passes on 1:1. So something else is going on. Can you select the image in InDesign and then Choose Object>image colour setting and see a profile there?
>ID does not support Grayscale profiles and puts the image on the Black plate of the CMYK working space
Ah yes, see how little I use greyscale that I forgot about that, the one of greyscales here in use are RGB ones, created with adjustment Layers in Photoshop. Peter is right - as always (well, mostly always ;-). )