Desilylation mechanism with fluoride
The mechanism is the same with the generation of the alkynyl anion as the abstract of this paper  ref 1 makes clear:


  Tetrabutylammonium triphenyldifluorosilicate (TBAT) can be employed as a fluoride source to cleave silicon−carbon bonds thus generating in situ carbanions that coupled with a variety of electrophiles, including aldehydes and ketones, in moderate to high yields. Among the examples reported is the first instance of fluoride-induced intermolecular coupling between allyltrimethylsilane and imine derivatives. Also, of particular note is the TBAT-initiated coupling of primary alkyl halides with allyltrimethylsilane. TBAT is an easily handled crystalline solid that has several advantages over tetrabutylammonium fluoride (TBAF) as a fluoride source; it is anhydrous, nonhygroscopic, soluble in most commonly used organic solvents, and less basic than TBAF. 


Bear in mind that the $\mathrm{p}K_\mathrm{a}$ of an alkynyl proton is approximately 25 (ref 2) so this is a far more stable anion than any possible alternative. Clearly with $\ce{MeOH}$ as the solvent it will be quenched immediately.