The reaction in black below was presented in a set of lecture notes as an example of the use of the Tebbe reagent, however it's not immediately obvious (to me, at least) that the product should be the gem-dimethyl compound shown.

I've used Tebbe in the past to turn ketones into terminal methylene groups, but never encountered what appears to me to be an over-reaction (though this is a known reaction).

Sadly the conditions given are vague, but based on the carbon count of the product, i'm going to assume that an excess of the Tebbe reagent was added.

In the first step we get the 'obvious' Tebbe olefination (I think). The Tebbe reagent will form the Schrock carbene which undergoes a '[2+2]' type process, with the formation of a 4 membered intermediate that breaks down to form the alkene and a Ti=O bond as a thermodynamic driving force.

If enough Tebbe reagent was added, I'm then assuming we get a second '[2+2]' type process, which would give a metallacyclobutane not too dissimilar to that found in a metathesis. What puzzles me is how this breaks down in the presence of heavy water to give the product shown, rather than just collapsing to give the (thermodynamically more favourable?) alkene product.

The reaction in black below was presented in a set of lecture notes as an example of the use of the Tebbe reagent, however it's not immediately obvious (to me, at least) that the product should be the gem-dimethyl compound shown.

Mechanistically, it appears that the Tebbe olefination has taken place once (standard formation of Schrock carbene, [2+2], retro [2+2] to give the alkene and a Ti=O compound as a thermodynamic driving force). The alkene must then however react with more Tebbe reagent (or more Schrock carbene) to form a metallacyclobutane. It's at this stage that I feel it makes less sense: firstly, what is the involvement of the deuterium oxide, but secondly and more importantly, why doesn't the metallacyclobutane just collapse back down to form the thermodynamically favoured alkene product.

I've used Tebbe in the past to turn ketones into terminal methylene groups, but never encountered what appears to me to be an over-reaction (I'd actually always considered Tebbe to be fairly mild and selective).

After some digging around in Comprehensive Organic Synthesis I, there is some mention of this 'over reaction' (1985JOC50). The authors report that treating the ketone 22 with 1 equivalent of Tebbe reagent affords a mixture of the expected methynlenation product along with some of the gem-dimethyl product (i.e. implying that an excess isn't required, but the reaction is just not overly chemoselective for the cyclic ketone over the cyclic alkene).

The reaction in black below was presented in a set of lecture notes as an example of the use of the Tebbe reagent, however it's not immediately obvious (to me, at least) that the product should be the gem-dimethyl compound shown. I've used Tebbe in the past to turn ketones into terminal methylene groups, but never encountered what appears to me to be an over-reaction.

Sadly the conditions given are vague, but based on the carbon count of the product, i'm going to assume that an excess of the Tebbe reagent was added.

In the first reaction then we get the 'obvious' Tebbe olefination (I think). The Tebbe reagent will form the Schrock carbene which undergoes a '[2+2]' type process, with the formation of a 4 membered intermediate that breaks down to form the alkene and a Ti=O bond as a thermodynamic driving force.

If enough Tebbe reagent was added, I'm then assuming we get a second '[2+2]' type process, which would give a metallacyclobutane not too dissimilar to that found in a metathesis. What puzzles me is how this breakdown in the presence of heavy water to give the product shown, rather than just collapsing to give the (thermodynamically more favourable?) alkene product.

The reaction in black below was presented in a set of lecture notes as an example of the use of the Tebbe reagent, however it's not immediately obvious (to me, at least) that the product should be the gem-dimethyl compound shown. 

I've used Tebbe in the past to turn ketones into terminal methylene groups, but never encountered what appears to me to be an over-reaction (though this is a known reaction).

Sadly the conditions given are vague, but based on the carbon count of the product, i'm going to assume that an excess of the Tebbe reagent was added.

In the first step we get the 'obvious' Tebbe olefination (I think). The Tebbe reagent will form the Schrock carbene which undergoes a '[2+2]' type process, with the formation of a 4 membered intermediate that breaks down to form the alkene and a Ti=O bond as a thermodynamic driving force.

If enough Tebbe reagent was added, I'm then assuming we get a second '[2+2]' type process, which would give a metallacyclobutane not too dissimilar to that found in a metathesis. What puzzles me is how this breaks down in the presence of heavy water to give the product shown, rather than just collapsing to give the (thermodynamically more favourable?) alkene product.