Silencers don't make a tink sound, regardless of what kind they are or where they're placed. Did you check your limbs for twist?
A hard string material (i.e., low stretch string) and or hard serving (monofilament, for example) leading to and around the string loops might also be a cause. Could be some sort of string slap. If you're shooting a recurve, moleskin in the limb tip string grooves, or a wool wrap around the string near the limb tips will quiet that noise.
Of course, if you have a two- or three-piece bow, the sound could be coming from the mating surfaces moving against each other at the conclusion of the shot. It can also make a click/tick at any point during the draw. Even a bow-mounted quiver can make that kind of noise. Lots of possibilities.
Addendum: Just noticed the bows you list under your avatar. I think most of those are hybrids or longbows. Some 3-piece. I'd put my money on bow generated noise rather than string noise. One way to find out/narrow it down is to take off the silencers. I suppose if the leather in the beavertails became severely dried out, it could produce a cracking sound as the bow is drawn. Doubt you would hear anything from it at release though.
From your description, i can't tell whether you're hearing the noise on the draw or at the conclusion of the shot. If it's at the draw, even an overly waxed string will make a "snick" as it pulls away from a recurve limb tip on the draw.