Many people will feel that the contacts keep shifting when they blink. I think it is not a serious problem. If the contact is not fit for you, you can choose another brand. Or you can apply some artificial tears to moisten your eyes. Maybe the dryness caused this. Hope you good luck!
It will take time to adjust to the shifting of the contacts. I think the contacts will attach to our eyeballs and will move with our eyeballs. But sometimes they will move in their own way. Just blink your eyes for several times again to try to replace them. And if this doesn't affect your vision, you can wear them for few days first. If you can't adjust to this, go and see an optometrist and talk with him or her.