I'm on modded minecraft and I tried to sort some items like a satchel from Thermal Expansion and few items from TInkers' Construct.

If I add a rule into InvTweakesRules like D1 6341 (a TiC pickaxed) it doesn't get sorted.
I've also tried to manually add an entry into the tree file without success.

Since 1.7 you need the 'id name' of the item, not the numerical ID. Press F3+H to display those, they should be something like 'amod:someitem'

Ah, addition: They probably need to be added to the tree file (and then use the name you assigned there) because it's somewhat ambiguous in the rules file now.