Hi scanlonp!
You may need to follow the instructions in this article to make sure all of your personal data is cleared from your previous phone:
What to do before selling or giving away your iPhone, iPad, or iPod touch
http://support.apple.com/kb/ht5661
It seems like this issue may stem from your iCloud account still being signed in on your old phone. Here is an article that can tell you how to sign out of your iCloud account on your iOS device:
iCloud: Change iCloud feature settings
http://support.apple.com/kb/PH2613
Turn off iCloud completely
Depending on whether you want to stop using iCloud on all or only some devices, do one or more of the following:
On your iOS device’s Home screen, go to Settings > iCloud, then at the bottom of the screen, tap Delete Account.
Note: If you delete your iCloud account, iCloud will no longer back up your iOS data. You can still back up your device in iTunes (for more information, open iTunes and choose iTunes > Help).
On your Mac, open iCloud preferences, then click Sign Out.
If your Mac has OS X v10.7.5 and you turn off iCloud, your calendar information and reminders aren’t stored locally in iCal. If you want to retain your calendar and reminder information, you need to back it up before turning off iCloud. For more information, see the Apple Support article iCloud: Calendar & reminder data removed from Calendar and Reminders or iCal when disabling iCloud Calendar.
On your Windows computer, open the iCloud Control Panel, then click Sign Out.
Note: If you turned on automatic download of music, app, or book purchases (in iTunes preferences or in Settings on your iOS device), your iTunes purchases are still downloaded to your devices.
Set up iCloud on your devices
Take care, and thanks for visiting the Apple Support Communities.
-Braden