Stainless steels are an interesting animal. Like others steels there are 1000s of stainless alloys. The Austenitic family is the only one (at least of the commonly available families) that ISNT magnetic and this is not due to lack or iron content (iron is still the principal ingredient) but rather the it is due to the "state" of the particles in its structure. Austenitic stainless isn't well suited to making firearm components however as is it typically soft (by comparison), often gummy to machine and galls easily if sliding/rotating upon similar material (ie a bolt cycling in a race way)
99% of all stainless rifles use Ferritic stainless steel which is magnetic. 416 being the most prevalently discussed grade in the firearms industry is used almost exclusively in making barrels and is common in receivers as well.
That said, I've not been privy to Tikka's drawings/material callouts but they will almost certainly be using the European designations for material. It'll be the same stuff (often slightly better) than the North American equivalents.
Where people often discuss one make of stainless rifle rusting or staining more readily than another, the difference will almost always be the environment they live in, the care they give their rifle and the surface finish of the rifle in question. Coarseness of bead blasting for example makes a huge difference on the retention of oil, dirt, sweat, salt etc. and will in turn affect the surface of that particular firearm's propensity to rust and corrosion.
If anyone is feeling nerdy and would like to read a little more about stainless families/grades, Unified Alloys has probably the best overview of the subject I've seen. It can be found on their website here:
https://www.unifiedalloys.com/blog/stainless-grades-families
Regards,
Paul.