I have gone over to Solstheim to begin questing. After a long hard day of questing I decided to rent a room at the Retching Netch and turn in for the night and wait for daylight (not that it ever gets dark, just more gloomy). Much to my surprise I got a loading screen and woke up on the other side of the island at one of those green stone shrines. Now I am wary of going to sleep again. I want to get some quests out of the way, and that will be somewhat harder if I am going to get sent to the other end of the island every time I want to get some shut eye. I also noticed that the townsfolk all seemed to head out to the green stone shrine at midnight. So I am guessing this Miraak guy has some kind of mind control thing that takes over when you go to sleep.

So, if you can tell me, without spoilers, do I need to do the MQ in order to be able to wake up in my own bed while sleeping on Solstheim?

BTW, I am not yet a dragonborn: I have not yet gone up to see the Greybeards.

I think it is random, I've went to sleep on solstheim 4 times and appeared at a stone 3 times.

If you sleep in the vicinity of a stone you will wake up at it. If you do the main quest a little bit though this can be rectified

I woke up on the opposite side of the island the one time I took a nap.

This also happens if you activate one of the stones before cleansing them. Several seconds later you will come out of your daze aft an animation showing you working on the stone for Miraak. It's just Bethesda's way to put the player into the danger of the rest of Solstheim's inhabitants.