Is PS color profile conversion function reliable?

I have a problem which driving me nuts for a long time.

I'm using CS5 with my monitor calibrated by Spyder2Pro and device ICC correctly be defined in Windows7 color management.

Expected if I convert a profiled picture to another color space, it will just the same as you preview it via soft-proofing with preserve RGB unchecked.
This is what soft-proofing designed to, right?

e.g.
My display system is AppleRGB compliant, I have a AdobeRGB picture and want to convert it to sRGB color space with preserve RGB unchecked, so in the target color space system user can

see my designed color whatever they are using color management or not.
Before conversion, I will preview the result by using soft-proofing function with preserve RGB unchecked. There will be slight color change due to the target gamut is narrower and this

is predicable.
After conversion, I use the soft-proofing function again to view the "converted sRGB picture" in target sRGB color space to make sure nothing wrong. The result is positive as you

expected.

However, the above seems 100% correct workflow doesn't work if your target color space gamut is wider than your source's!!!!

e.g.
An sRGB picture soft-proofing in target AdobeRGB color space with preserve RGB unchecked, there will be be no color shift due to the target space is wider in gamut.
So, I convert that sRGB picture to AdobeRGB profile and then use soft-proofing function again to view the "converted AdobeRGB picture" in the target AdobeRGB color space. But this time

the color shifted!!!!! It is different from my previous proofing result???

Is that PS color conversion incorrect????

You can do the same test by yourself, no need to have monitor calibrated as this problem actual happen btw PS's "Color space conversion" and its own "soft-proofing" functions

Hope that any expect can share your experience among this issue.

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Someone just told me, this problem is due to double profiling.
The same color profile of both input & output can't be using in proofing function and it's also unnecessary.