This is discussed, at least for dg-categories, in section 4 of Dyckerhoff's thesis: front.math.ucdavis.edu/0904.4713 where it is needed to understand LG models associated to isolated hypersurface singularities. It elaborates on Tyler's comment.

There is a lemma in Thomason's "Classification of triangulated subcategories" that says a category is tensor-closed if and only if it closed under tensoring by powers of an ample line bundle. Thus, Bondal-Orlov's reconstruction theorem is a consequence of Balmer's result. A proof of Bondal-Orlov's result along these lines is in Rouquier's notes - see paper 38 on his webpage. One caveat: Bondal-Orlov use only the graded structure of the derived category. With this argument, you need the triangles.

All the manifolds are still regular symplectic manifolds. We just change the coefficient field used in Floer homology. All we change is the field that is the receptacle for the counts of the numbers of pseudo-holomorphic polygons. For the elliptic curve case, we compare the Fukaya category, with coefficients in a $p$-adic field, of a real 2-torus to the bounded derived category of coherent sheaves of some other elliptic curve defined over that same $p$-adic field.

Good point Tim. This is one case where characteristic two is not necessarily our best friend.