Don't suppose you know what the old tiles are fixed to? Are they old quarries? Because some of those used to be laid in a cement mix which will be nearing its age of deterioration..... I think?
Is it Concrete is 75 years
Cement 50
Plaster 25
Or something.
(The lads will correct me)
If you're good to go with them yourself though, a cement-based adhesive it the way to go. Tubbed is for wall tiles only really, and only small wall tiles too. It sets by water evaporating from it, and you wont get that happen on a floor with a large tile. The edges of the tile will have set adhesive, and the centre of it will still be 'wet', and that causes shrinkage and the tiles will debond, fairly quickly too when in a high traffic area.
Cement cures by chemical reaction (when water is added) and it doesn't really matter how big the tile is providing you follow the instructions on the bag and mix the quantity right.
For small areas, for the cost of the bag of adhesive, it might be worth mixing the whole bag rather than trying to work out what a quarter of a bag would need water-wise. Kinda thing.
Again, wait for the lads to reply. I'd hate for you to go off my advice alone and me be wrong. As has happened quite a bit! (Me being wrong - thankfully I've been corrected quickly so I'm sure nobody used said wrong advice!! haha)