This is the first of a three-part series of papers, in which we study the
preheating phase for multifield models of inflation involving nonminimal
couplings. In this paper, we study the single-field attractor behavior that
these models exhibit during inflation and quantify its strength and parameter
dependence. We further demonstrate that the strong single-field attractor
behavior persists after the end of inflation. Preheating in such models
therefore generically avoids the "de-phasing" that typically affects multifield
models with minimally coupled fields, allowing efficient transfer of energy
from the oscillating inflaton condensate(s) to coupled perturbations across
large portions of parameter space. We develop a doubly-covariant formalism for
studying the preheating phase in such models and identify several features
specific to multifield models with nonminimal couplings, including effects that
arise from the nontrivial field-space manifold. In papers II and III, we apply
this formalism to study how the amplification of adiabatic and isocurvature
perturbations varies with parameters, highlighting several distinct regimes
depending on the magnitude of the nonminimal couplings $\xi_I$.
