Hello leetut,
I found an article that outlines how to access the tabs on your computer that are open on your phone. It sounds like you have it all setup correctly with Safari turned on in the iCloud settings on both devices with the same AppleID.
the name of the article is Safari 6 (OS X Mountain Lion): See your tabs from iCloud found here: http://support.apple.com/kb/PH11950.
If you have iCloud store your Safari bookmarks and Reading List, you can open the Safari tabs that are open on your other iCloud-connected devices. iCloud stores bookmarks together with a list of tabs that are open on each device.
- Open Safari if it is not already open.
- Click the iCloud Tabs button, and then click a tab you want to open.The iCloud Tabs button appears only if the Safari service is turned on in iCloud preferences.
(located at the top left of the Safari window.)
Safari doesn’t send your tabs to iCloud if you turn on Private Browsing.
and from the iPhone Users Guide, http://manuals.info.apple.com/en_US/iphone_user_guide.pdf, at the top of page 56 it outlines how to access iCloud tabs.
See webpages you have open on your other devices: Tap , then tap iCloud Tabs. To share webpages you have open on iPhone with your other devices using iCloud Tabs, go to Settings > iCloud and turn on Safari.
All the best,
Sterling