It's an interesting point about our intelligence of the situation of Tirpitz. PRU activity, Enigma decrypts and Norwegian resistance reports kept us reasonably well informed on the German big ships. In addition the departure of the Admiral and his staff could have been noticed by signals intelligence.
Her being shifted to Tromso from further north must surely be considered a retreat as her purpose in Kaafjord (and nearly all German surface navy activity so far in Norway) was to interfere with the Russian convoys. Dredging work took place at her new berth in order to prevent the ship capsizing, which could have been noticed by the Norwegians and perhaps by the PRU. Furthermore I don't think Tirpitz was provided with any destroyer escorts in the vicinity which would suggest at least she wasn't ready for sea.
No matter, the deed had to be done.
Here's Tirpitz on the way to Tromso with a black/grey/white camouflage.
This picture comes from this site:
German Navy in World War 2 - Kriegsmarine | World War Photos