(1) Suppose that $Z\subset X$ is a closed embedding, $U = X\setminus Z$ is the complement. If relevant, suppose that both $X, Z$ are smooth and even (if relevant) that the normal bundle of $Z\subset X$ is trivial. Then is it true that there is an exact triangle of complexes $K^* (Z)\to K^* (X)\to K^* (U) \to$? Here by $K$ theory I mean (connective) K theory of the category of perfect complexes. For what I need (this came up in the context of trace formulae), rational coefficients are enough. I found many places where very similar results are written down, but not this one explicitly.

(2) Suppose that, further, in the example above we have a (suitably flat) sheaf of smooth, compact (DG) algebras, $\mathcal{A}$, over $X$. Then we can study $K$ theory of categories of bundles of $\mathcal{A}$-modules over the three spaces. Again, is it true that these fall into an exact triangle as above?

It seems like both of these statements should follow from some colimit-compatibility of the $K$ theory functor, but I can't find a reference.