Our local verditius wants to install a spell (Incantation of the Milky Eyes) that he actually knows into a device.
No problems so far.
But now he wants to spend the exposure XPs towards mastery of said spell. Any objections?
It bothers me a little, but I can't put my finger on why.
I'd say no because: this is not the spell you put in. You use the arts, MT and your previous knowledge to give ideas (similar spell bonus) but you are not improving your "same" spell.
In the same way, when you develop a spell, you can't put 2xp in his mastery score or a mastery for a similar spell
In principle, I'd agree. This seems to be the RAW. In practice... why not give the player some slack? It's a measly 2 xp, why not let him invest it in stuff other than Magic Theory?
I also think it's reasonable to allow. As mentioned it's only 2 XP. It's also quite fitting, I think, that his understanding of a spell is improved by spending months and months working on having a magic item reproduce it. If he didn't already know the spell or was in the process of inventing I'd think it less fitting, but he already knows it and is probably casting it again and again in the lab (to get further under the skin of the effect).
If it's only 2 xp, don't stress it. If there's any reasonable excuse, then let them have it. A SG has to work with the Troupe's desires, as well as shepherd their direction. A good story includes winks at their desires, as well as challenges that prevent them too easily - some of the small stuff is not worth the effort to put a speedbump in front of it. 
I agree that the placement of two xp is not worth upsetting the player about and in your situation I'd let the player get his spell mastery xp.
I also agree that the justification for putting the xp into spell mastery doesn't jibe with the setting. The character is creating an item to duplicate the spell, they're only using the spell as a vague reference. they aren't casting the spell at all. To me, spell mastery is about mastering that one formulaic spell and the item uses a different formula (OK, I'm moving away from rules towards interpretation here). The insight that a character gets from creating an item that duplicates the spell seems to me to be much better reflected by putting the xp into one of the related arts.
To use an analogy, when I was younger I spent a ridiculous quantity of hours trying to become a better musician, and while learning a given etude may have helped me master a piece of music that used similar phrases, it did it by increasing my score in "perform material similar to the etude" not in "perform specific related piece of music".
I've got to disagree with you there - I'd say it's perfectly in keeping with the setting. After all, formulaic spells can be tinkered with in many, many ways once learned - changing targets, auras, using a Talisman, Vis boosting, Mastery options, Flexible Formulaic Magic and so on. Rigid Magic, in contrast, is a Major Flaw. A magus can, after all, cast any non-Ritual spell with standard parameters by spontaneous magic, though he may be need to be very lucky in the attempt. A formulaic spell is, rather than a fixed method of casting (which would immediately make quiet or still casting impossible, not to mention all the other vanilla spell tinkering possible), a well understood effect, with limited and defined parameters, certainly potentially incorporating rigidly defined, efficient magical methods, which because it is so well understood can be easily and swiftly adapted to the current situation so as to take full advantage of a magus' Arts. Mastery of a spell indicates a still deeper understanding, and this is why regardless of who wrote a book on Spell Mastery, every reader may take away a different knack or Mastery option.
As such, provided it is exactly the same effect he is trying to instil into the item, doing so should allow him to put the XP into Mastery - rather than learning more of Ignem in general, or Magic Theory in general, he has concentrated on this spell in the specific and come closer to mastering it. If the effect is not identical, however, then I'd disallow it - you've changed the parameters and whilst it's still a related effect and you'd get that bonus, you are no longer studying the same effect in great detail.
I'd allow it. It really isn't going to break anything and it gives the player what they want. Remember, increasing Abilities is a hard business and can be really frustrating to the player when they end up one or two points away from where they want to be.
Actually, there is absolutely no foundation for that assumption - what goes on in the lab is completely undefined. Maybe they cast the spell regularly, maybe need it for reference, maybe not so much, maybe maybe (but only "maybe").
Your saga, your interpretation - but as you (later) say, that's all it is. 