Really? "-atok" is not listed as a version of the suffix? It does not feel like an exception. But it may be rare. Here, the word is "kanál", and the last vowel ("á") gets shortened to "a" when the suffix is added. But this is not the only word that does that.
kanál - kanalatok (spoon)
pohár - poharatok (drinking glass)
But there are other words, that do not shorten, and, still, they get the "-atok" suffix:
láb - lábatok (leg)
ágy - ágyatok (bed)
agy - agyatok (brain)
vágy - vágyatok (wish/desire)
kád - kádatok (tub)
tál - tálatok (bowl)
hát - hátatok (back)
Actually, the suffixes are -tok, -tek, -tök. And there can be a buffer sound between the word and the suffix, to ease the pronunciation. So, that is how we can end up with "-a-tok". It is the "-tok" suffix with the buffer sound "a".
You might also be thinking of conjugation of verbs here, where the suffixes are quite similar to the possessive ones, but not exactly the same.
To add to vvsey's explanation: the binding vowel is usually the same that is used when adding the -t suffix to the base noun:
- ház - házat - házam
- kanál - kanalat - kanalad
- könyv - könyvet - könyvetek
Doesn't work for nouns that don't have a binding vowel for the -t suffix, though: hús - húst - húsom
Are you all sharing one spoon, or would "Your spoons are small." be a valid translation? The "kicsi" needs to match, in plurality, "A ti kanalatok", so that, in itself, is not an indication that you share one spoon. I'd have thought that "A ti kanalatok" could mean one spoon each, as when they are talking about people in coats, they translate that into the singular. I didn't try plural here, as it was rejected previously in a very similar translation.