ImageMagick is trying to be clever, and keep track of an image position within a logical screen. There's probably a way to tell it not to do that -- maybe someone else can help.
Also...
Your f2.gif is not a valid GIF file. The GIF89a spec says:
Each image must fit within the boundaries of the Logical Screen
f2.gif's logical screen is 65x93. It contains one image, whose size is 65x93, and whose position is (60,872), which is way beyond the boundaries of the logical screen. I'd say it's a bug that IM is willing to create an invalid GIF image.
Also...
Your f.tif file includes XPosition and YPosition tags, which must be what IM bases f2.gif's image position on. However, the ResolutionUnit tag in f.tif is "unspecified", which effectively makes the Position tags meaningless. I guess that IM treats them as if they were in inches, which is the default unit for TIFF files, but I don't think it's supposed to do that. The default of "inches" should only be used if the ResolutionUnit tag is not present, not if it's present but indicates "unspecified". So I think that's another bug.