Update: Short answer is the issue is fixed in SharePoint 2013. I haven't verified this yet.
Long answer is it's recorded as MS internal bug: "Office14 459444 - MOSS-IP : Partner Controls are not hooked up to IPFS selection model/service infrastructure"
RESULTS: tabbing away [from people picker] causes a postback (expected) but when the page reloads the focus is reset to the top of the form, so we can never tab to the button
EXPECTED: after the postback, the tab focus should return to the next item in line (i.e. the Resolve icon of the people picker, then the Browse icon, then the Button)
Update: It seems any post-back on the form will cause the people picker to go into auto-resolve mode and cause the tab-back problem. For example, we have some cascading-drop-down lists and when we re-query for the dependent drop-down, the non-required people pickers start to exhibit the problem.
Update: Problem is also reported here.
Update: I posted an update here. Basically nothing new from MS. Our current workaround is to "de-require" the people picker and then use a "fake" single line of text field to simulate the required behaviour. We can also a section to show hide a red required asterisk based on the presence of the value.
Update: We've logged this as a bug with Microsoft. It seems to happen if you have a required People Picker on the page. They confirmed the bug - but they're doing further investigation atm. I hope to get answer soon.
For us, this is caused by a full page post-back. We are using a SharePoint 2010 in the old SharePoint 2007 Visual Styles (v3), and so the AJAX Update Panel isn't present in the Master Page (hence the full page post-back).
Explicitly setting the tab order didn't work.
We are now investigating upgrading this site to use the v4
UIVersion/master page styles.
Interestingly in the old styles, the control attempts to resolve the user after you tab out of the people-picker, however in the new version, it doesn't seem to resolve the user until you click the resolve button or hit save. Seems it'd be nice to have that option.