What happens when you accidentally sign in to xbox, play with it and earn achievements on...

When playing a game in offline mode (not signed in to XBL), any achievement/progress earned/made will be saved in a way, but only when you play it in offline mode i believe. With halo it is quite problematic, to get any progress saved when in offline mode
as you need to be signed into Xbox Live for the servers to recognize you and your progress made. In my opinion you will need to do it again, or wait a few days/weeks for the servers to backtrack your record and find it, and give you the rewards for it.

Whereas Achievements that are earned in offline mode, will be updated to your account next time you sign in to Xbox Live.

This happened to a friend of mine so i know what its like.

Hmmm... sounds as though there was an connection issue. Sorry about the loss of your achievements, I know that feeling. Had this happen to myself long ago so hopefully I can explain it well.

Well the theory I have that happened is an offline achievement loss. If you earn achievements offline on a console, be sure you sign into Xbox Live using that console since it only keeps your progress in achievements when you were last connected to XBL with
that profile. So if you recover your account or play on a different Xbox; it will overwrite and disable other locations where you last used your profile meaning the achievements you earned offline is loss and needs be re-earned. I'm not entirely sure if this
applies to the Xbox One or not, but this is the only thing I can think of that happened.

Well, this only applies if you have to re-download your account after you got offline achievements, but if you earned ALL of your achievements offline, and then re-downloaded your account BEFORE you signed-in with those achievements earned, you lose all
of them. I'm pretty sure this is what happened to you.

Are you playing the game offline or online when you earn the achievements? In other words are you signed into XBL?

Achievements unlocked offline do not usually load up when you sign back in to Live. However, what you should do is play some games and earn some new achievements. Perhaps the others will load up over time as you play online more.