Color of precipitate formed on reaction of acetylene with Tollen's Reagent
You are correct that ammoniacal silver nitrate is Tollen's reagent. Tollen's reagent is most notable for its reaction with aldehydes to produce a silver mirror, but it also reacts with several other types of compounds, notably alpha-hydroxy ketones and terminal alkynes.

With terminal alkynes, the alkyne reacts as a acid to form a silver acetylide which precipitates. In the case of acetylene, both hydrogens can react: $$\ce{HC#CH + 2AgNO3 + 2NH4OH -&gt; AgC#CAg + 2NH4NO3 + 2H2O}$$

The colour of the precipitate is variously described as yellow, gray-white, or white. The actual colour you observe is probably strongly dependent on the purity of the sample and the size of the precipitated particles.