Back in the day, when this was a more popular product, I laid 1000's of sq/m of this stuff.
Saltillo Mexican terracotta. (Named after the town which is famous for it's production).
It is made in molds and left out in the sun to dry simply plied up on top of each other. The yellow tiles are actually the ones sat on the top of each pile and far more exposed to the sun and bleached basically.
If you treat with boiled linseed oil, don't just keep slapping it on, it will simply keep soaking it up, as you found out. Two coats with a paint roller are enough, then allowed to "cure" overnight. The oil congeals in the tile overnight and acts as an impregnating sealer.
So you've laid it, oiled it again, and it's still sucking up oil. That's normal, leave it overnight again before you grout. It doesn't matter if there is oil residue as the coarse grout you need to use with this width joint will clean off the top of the tile surface. We never used to dilute the oil, always used neat.
Give it a good clean, leave it overnight.
If the customer then wanted a finish, we would avoid wax as it was very labour intensive and never lasted a great deal of time without looking rough. So we would use HG Golvpolish, just wipe it on and allow it cure, it would create a warm satin finish, like wiping vegetable oil over the surface and bringing out the colour. It had the advantage of being removable so once a year it could be stripped and re done.
HG decided after years of using this stuff it was no good for terracotta (never knew why though) so replaced it with a bespoke product. HG Shine Seal, which I'm pretty sure does exactly what Golvpolish did.
Oh, and never ever screw up a rag or towel coated in linseed oil, the self combust. My partner at the time burnt his van out having done this once, Fire brigade out, neighbours gawping the lot!