In general, more substituted alkenes are more thermodynamically stable. However, in certain cases such as enamine alkylation, the less substituted double bond is favored. How do we know that which is favored during a particular reaction? Can we have a generalized rule for it?
I'll address your concerns about alkene stability in general and enamines in particular. It is useful to examine the acyclic permutations of C6H12. The heat of formation of these isomers is a good measure of their relative stability. As the double bond is increasingly substituted with alkyl groups, the heat of formation becomes more negative, i.e., more stable. Tetrasubstitution is better than trisubstitution which is better than disubstitution. Clearly, monosubstitution is the least desirable case. The stabilization by alkyl groups in this case is due to the hyperconjugation of the bonding σ-CH orbital and the anti-bonding π*orbital. The more opportunities for this interaction, the more the stabilization. Heats of formation are available at the NIST site.
The pyrrolidine enamine of 2-methylcyclohexanone prefers the trisubstituted over the tetrasubstituted position. Because there is a strong resonance contribution (planarity) in the enamine, the tetrasubstituted isomer has strong steric interactions between the methyl group and the methylene adjacent to the nitrogen in the pyrrolidine ring. The equilibrium is not spontaneous but it is catalyzed by water or traces of acid. In the trisubstituted isomer, the methyl group adopts an axial position to avoid an A1,3 interaction if the methyl group were equatorial.
I'm not sure where the alkene is during enamine alkylation. I can only see an alkene in the enamine starting material, so I will try to explain the alkene formation selectivity for enamine formation.
The less substituted alkene is favored for enamine formation because in the enamine, the N atom pushes electron towards the alkene by resonance. A less substituted carbon atom accommodates the negative charge better than a more substituted carbon atom, so a less substituted alkene is more stable in this case.
For other reactions such as alcohol dehydration, the more substituted alkene is formed because the intermediate has a carbocation character. The more stable intermediate is the more substituted intermediate, thus giving the more substituted alkene as the major product.