First off, I think this post would be better in the inorganic chemistry forum.
I don't know very much about tetramethyltin, but I can give you some food for thought about dimethylzinc. I've worked with diethylzinc.
In general, carbanions are very strong bases. In air, you have water. Being a very strong base, carbanions will rapidly deprotonate water creating the corresponding alkane and hydroxide. This releases a lot of heat and can be the origin for many organometallic reagents to be pyrophoric (heat release + high local concentration of combustible alkanes). For dimethylzinc, as you said--is linear. Zn2+ tends to form tetrahedral complexes, thus dialkylzinc compounds are coordinatively unsaturated. This means that there are open coordination sites for a Lewis base/ligand to attack. So molecules such as water can easily coordinate the Lewis acidic zinc, and subsequently protonate the alkyl group to create an alkylhydroxozinc. I know that diethylzinc reacts with oxygen as well. I'm not too clear about what happens then, but I do believe at least one of the ethyl groups becomes an ethoxy group.
As for tetramethyltin, I can't make any real statements (though I'm curious to investigate this more when I have time), but I'll give you a couple thoughts. The Lewis acidity of tetramethyltin might just be too low to react with water (and maybe oxygen) rapidly enough to be pyrophoric. Steric hindrance as you mentioned, may be a factor, with analogies to substitution of a tert-butyl halide being slow due to sterics, but tin is a lot larger than carbon, and so it should be easier to attack than an electron deficient carbon. In short, I'm not sure, but I hope someone this gives you something to think about or lead you in the right direction.
If anything I said was confusing, I would be happy to clarify with more detail.