When a contact record is pulled using REST API, for "Birthday" field the value will be in date/time format ex: 2015-01-02T18:30:00Z even though the date configured in Office365 is "2015-01-03".

Is this right behavior w.r.t office365 working?

No, this is a problem. We're working on addressing this. The problem you're seeing is because the field is implemented as a DateTimeOffset, so it gets shifted to UTC from the time zone the contact was created in. Thanks for letting us know!

Thank you for the update Jason.

When can I expect the fix? any time frame ?

I don't have a timeframe unfortunately.

I have one more issue, when I try to update Birthday field value through Office365 REST API the value is not getting updated. Can you suggest me any workaround to get the issue fixed.

I am not sure if I am sending proper format because the documentation says field type is "datetimeoffset" but the example they have suggested sends only "date" as its value. I tried both the ways but failed to achieve the result.

It's working OK for me. I sent PATCH requests with both this format:

{
  "Birthday": "1992-07-22T04:00:00Z"
}

And this format:

{
  "Birthday": "1991-07-22"
}

Both requests succeeded and the value gets set (confirmed by doing a GET on the contact afterwards). I did find one bug though: Outlook Web App is showing the old value. Outlook shows the new value, so there's something missing there. I've reported it to our developers.