Have always heard from Tikka owners that they were getting good to excellent accuracy.
Finally have a lh T3 in 338 Federal. It is only shooting 1 1/2" groups with the Federal 200 gr Fusion ammo, while the previous owner showed me targets of 1/2" with the Federal 180 gr AccuBond ammo. Unfortunately I cannot find any of that at the moment. Still have to try the Federal 200 gr Uni-Cor ammo and the 210 gr Nosler Partition ammo I have on hand. Not worried about its accuracy yet, as I am not done with its testing. Then there will be load development to come up with its best load.
Point is, every rifle has a preference, and it just take some experimenting to find your rifle's preferred load.
Have you tried any other ammo yet?
A question I would also ask, is how long are you taking between shots in your testing? 2 minutes, or shooting the 3 shots as quickly as you can?
If quickly, then I would think that it is a bedding issue and your barrel is heating up and the barrel is touching the stock or some other pressure point as suggested above that is causing the third shots to consistently be out of the group.
If not this, then as others have stated above, there are a number of tests to try to help determine the problem.