New, created contacts sync, but imported contacts do not, towards exchange
Is Contact syncing enabled in Settings/(accounts)/Corporate/(your exchange account)? 

View one of the contacts and go to menu/edit. At the very top, does it show that it is attached to the exchange account or the Google account? If it is the Google account, you need to make sure to select the exchange account when adding the contacts. If it does show the exchange account and syncing is enabled, edit your comment to reflect this for further support.