I've been working on a EE 2.7.0 site that uses the latest Profile:edit and has this password reset form, and I've never seen the issue you're describing.
If this were happening on just one page, I'd say that it sounds like maybe you have EE access restrictions set on your Reset Password page, with the restriction's "unauthorized" redirect pointing to the site homepage. Have you checked for this in the EE Template Manager?
If it's happening on multiple pages, and on pages with no EE access restrictions, then I don't know what's up -- again, I've never seen this issue.
updated: added the EE version.