From my experience, there could be only one URL with "https" protocol on MySiteA, which returns 200 OK (since there is no redirect for https protocol) and unless you are using absolute links when interlinking on your pages, that one single URL will cause all other links on that page to use "https" protocol.
That "https" link could be an external link from somewhere, an incorrect link on your MySiteB or it could have been a small window where Google managed to find such URL in the past (eg. incorrect linking somewhere within your site to [
MySiteA...] which may even be corrected since). As such request (to [
MySiteA)...] returns 200 OK and is not redirected, Google may keep requesting it for a long time and from it can potentially get other links that would now be https on MySiteA.
Sometimes it is hard (or even impossible) to find where such mistake originated, but correct redirection between https/http from MySiteA to MySiteB will fix this problem eventually as it will tell Google that this page is now moved permanently to a new location.
You can try to run xenu link sleuth against your MySiteB to see if you can detect something and correct if you do, but as I said, even if the linking error is not there any more, if Google picked it up, it has this URL from MySiteA as a valid URL that returns 200 so it may keep re-requesting it.
If both sites point to the same webspace (which you say they do) then the same ISAPI rules will get executed for requests that arrive to either MySiteA or MySiteB and it is up to you to ensure that you have correct redirection rules set - be careful as this can be easily mess up unless you know exactly what you are doing.
Yes, ISAPI redirect will get executed for all requests for [
MySiteA...] regardless whether the redirect is from browser or from bot, so, if set up correctly, it will work when you click on your link showing when you run "site" command. If it does not work from your result in "site" command, then it just does not work, fullstop.
And lastly, why just some of your https pages from MySiteA are showing in "site" command - there could be many reasons. Google filtering pages is one, the second may be that just some of them are able to be requested as "https" (depends on your internal linking structure) etc.